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All questions of System of Equations for EmSAT Achieve Exam
Can you explain the answer of this question below:The value of m, if a = 3 and b = 1 is the solution of equation 2a + 3b = m is:
- A:
9
- B:
10
- C:
8
- D:
7
The answer is a.
The value of m, if a = 3 and b = 1 is the solution of equation 2a + 3b = m is:
9
10
8
7
|
Abdul Hadi answered |
In the given question we have 1 a=3,b=1 the given equation is 2a 3b=m by substitute the values of a,b we get 2×3 3×1=m so the value of m= 9 the answer is a
If the line represented by the equation 3x + αy = 8 passes through the points (2,2), then the value of α is- a)0
- b)4
- c)3
- d)1
Correct answer is option 'D'. Can you explain this answer?
If the line represented by the equation 3x + αy = 8 passes through the points (2,2), then the value of α is
a)
0
b)
4
c)
3
d)
1
|
Jaya Khanna answered |
3x+ay=8
Since it passes through point (2,2),
Hence, (3*2)+(a*2)=8
Or, 6+2a=8
Or, 2a=8-6
Or, 2a=2
Or, a=2/2
Or, a=1
The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is:
a) 6
b) 5
c) 7
d) -7Correct answer is option 'C'. Can you explain this answer?
The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is:
a) 6
b) 5
c) 7
d) -7
a) 6
b) 5
c) 7
d) -7
|
Ananya Sharma answered |
If x = 2, y = 1 is a solution of the equation 2x + 3y = k, then these values will satisfy the equation. So, putting x = 2 and y = 1 in the equation, we get
2(2) + 3(1) = k
⇒ 4 + 3 = k
⇒ k = 7.
x = 2, y = – 1 is a solution of the line equal to :
- a)2x + 3y = 5
- b)x + y = 5
- c)x + y = 1
- d)x – y = 9
Correct answer is option 'C'. Can you explain this answer?
x = 2, y = – 1 is a solution of the line equal to :
a)
2x + 3y = 5
b)
x + y = 5
c)
x + y = 1
d)
x – y = 9
|
Bhaskar Chatterjee answered |
Sorry, I cannot provide a practice test/quiz or MCQ (Multiple Choice Questions) with solutions without knowing the specific chapter or subject you are referring to.
Rainwater harvesting system is a technology that collects and stores rainwater for human use.Anup decided to do rainwater harvesting. He collected rainwater in the underground tank at the rate of 30 cm3/sec.
Q. Write the equation in standard form.- a)30x – y + 0 = 0
- b)30x + y + 0 = 0
- c)30x – y – 0 = 0
- d)30x – y = 0
Correct answer is option 'A'. Can you explain this answer?
Rainwater harvesting system is a technology that collects and stores rainwater for human use.
Anup decided to do rainwater harvesting. He collected rainwater in the underground tank at the rate of 30 cm3/sec.
Q. Write the equation in standard form.
a)
30x – y + 0 = 0
b)
30x + y + 0 = 0
c)
30x – y – 0 = 0
d)
30x – y = 0
|
Let's Tute answered |
Rainwater is collected in the underground tank at the rate of 30 cm³ / sec
Water collected in 1 sec = 30 cm³
Water collected in x secs = 30x cm³
Water collected in x secs = y cm³
=> y = 30x
a linear equation y = 30x
30x - y = 0 ,30x -y +0=0
is standard form
Which of the following is a solution of the equation 4x + 3y = 16?- a)(1, 3)
- b)(2, 3)
- c)(2, 4)
- d)(1, 4)
Correct answer is option 'D'. Can you explain this answer?
Which of the following is a solution of the equation 4x + 3y = 16?
a)
(1, 3)
b)
(2, 3)
c)
(2, 4)
d)
(1, 4)
|
Vikas Kapoor answered |
Given equation is :
4x + 3y = 16
Putting x = 1 and y = 4
4 .1 + 3. 4 = 16
4 + 12 = 16
16 = 16
So option D is the correct answer.
An equation of the type ————- represents a line passing through the origin.- a)y = m + x + 1
- b)y = m + x
- c)y = mx
- d)x = m – y
Correct answer is option 'C'. Can you explain this answer?
An equation of the type ————- represents a line passing through the origin.
a)
y = m + x + 1
b)
y = m + x
c)
y = mx
d)
x = m – y
|
Mohit Verma answered |
It seems that the rest of the question is missing. Can you please provide more information or context?
Can you explain the answer of this question below:The point lying on the equation 2x – y = 5 is:
- A:
(3, 4)
- B:
(-3, 1)
- C:
(6, 1)
- D:
(2, -1)
The answer is d.
The point lying on the equation 2x – y = 5 is:
(3, 4)
(-3, 1)
(6, 1)
(2, -1)
|
|
Let's Tute answered |
The point will lie on the line if L.H.S of the equation is equal to R.H.S
Given equation is 2x - y = 5
Put the point ( 2 , -1) in the above equation
2 . 2 - (-1) = 4 + 1 = 5 = R.H.S
So this proves that the given points lie on the line.
So option D is correct answer.
Can you explain the answer of this question below:If -0.25x + 1.3 = -0.55x – 0.2 , then x
- A:
-2
- B:
-5
- C:
5
- D:
2
The answer is b.
If -0.25x + 1.3 = -0.55x – 0.2 , then x
-2
-5
5
2
|
Vp Classes answered |
Given equation is :
-0.25x + 1.3 = -0.55x – 0.2
-0.25x + 0.55x = -0.2 - 1.3
0.30 x = -1.5
So x = -1.5 / 0.30
x = -5
So option B is correct answer.
Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?
- a)4km/hr
- b)6km/hr
- c)3km/hr
- d)7km/hr
Correct answer is option 'B'. Can you explain this answer?
Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?
a)
4km/hr
b)
6km/hr
c)
3km/hr
d)
7km/hr
|
|
Ananya Sharma answered |
Upstream = (x-y) km/hr
Downstream =(x+y)km/hr
20(x+y)=2
X+Y=10.....(1)
4(x-y)=2
x-y=2....(2)
Solve both equations
x+y=10
x-y=2
2x=12
X=6
Substitute x=6in i
6+y=10
Y=4
Speed of rowing in still water is 6km/hr.
the speed of still water is 4km/hr
So option B is correct answer.
Find value of a and b if y = 1 and x = 2 is solution of linear equation ax + by =3 and 3a – 2b = 1.
- a)a = 2, b = 3
- b)a = 1, b = 2
- c)a = 1, b = 1
- d)a = 4, b = 1
Correct answer is option 'C'. Can you explain this answer?
Find value of a and b if y = 1 and x = 2 is solution of linear equation ax + by =3 and 3a – 2b = 1.
a)
a = 2, b = 3
b)
a = 1, b = 2
c)
a = 1, b = 1
d)
a = 4, b = 1
|
|
Amit Sharma answered |
Given Equations
ax + by = 3 {1}
3a - 2b = 1 {2}
x = 2, y = 1 ( given)
Equation {1} becomes,
2a + b = 3 {3}
Substract equation {3} from {2}, we get,
2a + b - 3a + 2b = 3 - 1
-a + 3b = 2
3b = 2 + a
b = (2+a) / 3
Put the value of b in equation {3}, we get
2a + (2 +a ) / 3 = 3
(6a +a +2) / 3 = 3
7a + 2 = 9
a = 1
Now put value of a in {3}
2 + b = 3
b = 1
hence we get value of a and b i.e. 1 and 1
The Equation y = – 5, in two variables can be written in the form of ax + by + c = 0 as- a)1.x + 0.y + 5 = 0
- b)0.x + 1.y -5 = 0
- c)0.x + 1.y + 5 = 0
- d)1.x + 0.y -5 = 0
Correct answer is option 'C'. Can you explain this answer?
The Equation y = – 5, in two variables can be written in the form of ax + by + c = 0 as
a)
1.x + 0.y + 5 = 0
b)
0.x + 1.y -5 = 0
c)
0.x + 1.y + 5 = 0
d)
1.x + 0.y -5 = 0
|
Tarun Goyal answered |
Y = -5
=> y + 5 = 0
=> 1.y + 5 = 0
=> 0.x + 1.y + 5 = 0 C)
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : There are infinite number of lines which passes through (3, 2).Reason : A linear equation in two variables has infinitely many solutions.- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'B'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : There are infinite number of lines which passes through (3, 2).
Reason : A linear equation in two variables has infinitely many solutions.
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
|
Swati Verma answered |
We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.
Through a point infinite lines can be drawn.
Through (3, 2) infinite number of lines can be drawn.
Hence, Assertion is also correct.
But reason (R) is not the correct explanation of assertion (A).
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
Which of the following is not true?- a)The coefficients of x and y in a linear equation in x and y must be rational numbers.
- b)There’s only one set of values of x and y that satisfy a linear equation in x and y.
- c)A linear equation is an equation of first degree
- d)For a linear equation in x the coefficient of y is zero.
Correct answer is option 'A'. Can you explain this answer?
Which of the following is not true?
a)
The coefficients of x and y in a linear equation in x and y must be rational numbers.
b)
There’s only one set of values of x and y that satisfy a linear equation in x and y.
c)
A linear equation is an equation of first degree
d)
For a linear equation in x the coefficient of y is zero.
|
Arizona Academy answered |
The coefficients of x and y in a linear equation in x and y must be rational numbers.
The condition is only about the power of the variables being one and both coefficients not being zero at the same time. So as long as the coefficients are real numbers, the equation can be a linear equation.
Can you explain the answer of this question below:The positive solution of equation ax + by + c = 0 always lie in the:
- A:
3rd quadrant
- B:
Ist quadrant
- C:
4th quadrant
- D:
2nd quadrant
The answer is b.
The positive solution of equation ax + by + c = 0 always lie in the:
3rd quadrant
Ist quadrant
4th quadrant
2nd quadrant
|
|
Ananya Sharma answered |
The solution of the linear equation is represented by the ordered pair (x, y).
If x > 0, y > 0, then solution lies in first quadrant.
(2,-3) is a solution of 3x + 4y + k = 0. So, the value of k must be- a)-6
- b)6
- c)-4
- d)4
Correct answer is option 'B'. Can you explain this answer?
(2,-3) is a solution of 3x + 4y + k = 0. So, the value of k must be
a)
-6
b)
6
c)
-4
d)
4
|
Anika Reddy answered |
To find the value of k, we can substitute the given solution (2, -3) into the equation and solve for k.
Substituting the values of x and y into the equation:
3(2) + 4(-3) + k = 0
Simplifying the equation:
6 - 12 + k = 0
-6 + k = 0
k = 6
Therefore, the value of k is 6.
Explanation:
To determine the value of k, we can use the given solution (2, -3) and substitute it into the equation 3x + 4y + k = 0. The values of x and y represent the coordinates of the solution point.
Substituting the values of x and y into the equation, we get:
3(2) + 4(-3) + k = 0
Simplifying the equation gives us:
6 - 12 + k = 0
Combining like terms, we have:
-6 + k = 0
To isolate k, we can add 6 to both sides of the equation:
-6 + k + 6 = 0 + 6
Simplifying further:
k = 6
Therefore, the value of k is 6.
Substituting the values of x and y into the equation:
3(2) + 4(-3) + k = 0
Simplifying the equation:
6 - 12 + k = 0
-6 + k = 0
k = 6
Therefore, the value of k is 6.
Explanation:
To determine the value of k, we can use the given solution (2, -3) and substitute it into the equation 3x + 4y + k = 0. The values of x and y represent the coordinates of the solution point.
Substituting the values of x and y into the equation, we get:
3(2) + 4(-3) + k = 0
Simplifying the equation gives us:
6 - 12 + k = 0
Combining like terms, we have:
-6 + k = 0
To isolate k, we can add 6 to both sides of the equation:
-6 + k + 6 = 0 + 6
Simplifying further:
k = 6
Therefore, the value of k is 6.
For two lines 2x + y = 1 and x – y = 2 if the x coordinate of the common point is 1 what is the y coordinate?- a)-1
- b)2
- c)-2
- d)3
Correct answer is 'A'. Can you explain this answer?
For two lines 2x + y = 1 and x – y = 2 if the x coordinate of the common point is 1 what is the y coordinate?
a)
-1
b)
2
c)
-2
d)
3
|
Rishika Nambiar answered |
Solution:
Finding the y-coordinate of the common point:
Given two lines:
2x + y = 1 ... (Equation 1)
x - y = 2 ... (Equation 2)
We are given that the x-coordinate of the common point is 1.
Substituting x = 1 in Equation 2, we get:
1 - y = 2
y = -1
Therefore, the y-coordinate of the common point is -1.
Final Answer:
Option (a) -1 is the correct answer.
Finding the y-coordinate of the common point:
Given two lines:
2x + y = 1 ... (Equation 1)
x - y = 2 ... (Equation 2)
We are given that the x-coordinate of the common point is 1.
Substituting x = 1 in Equation 2, we get:
1 - y = 2
y = -1
Therefore, the y-coordinate of the common point is -1.
Final Answer:
Option (a) -1 is the correct answer.
Temperature is a measure of the warmth or coldness of an object or substance with reference to some standard value.In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius.An equation that converts Fahrenheit to Celsius is:
On reading the above information, some queries come in Aman’s mind. Help him to resolve his following queries:Answer the following :Q. If the temperature is 30°C, what is the temperature in Fahrenheit ?- a)80°F
- b)82°F
- c)86°F
- d)90°F
Correct answer is option 'C'. Can you explain this answer?
Temperature is a measure of the warmth or coldness of an object or substance with reference to some standard value.
In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius.
An equation that converts Fahrenheit to Celsius is:
On reading the above information, some queries come in Aman’s mind. Help him to resolve his following queries:
Answer the following :
Q. If the temperature is 30°C, what is the temperature in Fahrenheit ?
a)
80°F
b)
82°F
c)
86°F
d)
90°F
|
|
Swati Verma answered |
= 54 + 32
= 86
The linear equation 2x + 5y = 8 has:- a)A unique solution
- b)Infinitely many solution
- c)No solution
- d)Two solution
Correct answer is option 'B'. Can you explain this answer?
The linear equation 2x + 5y = 8 has:
a)
A unique solution
b)
Infinitely many solution
c)
No solution
d)
Two solution
|
Shambhavi Singh answered |
Explanation:
The given linear equation is 2x + 5y = 8. To determine the number of solutions, we can convert this equation into slope-intercept form.
2x + 5y = 8
5y = -2x + 8
y = (-2/5)x + 8/5
Now we can see that the equation has a slope of -2/5 and a y-intercept of 8/5. This means that the equation represents a line in the coordinate plane.
Infinitely many solutions:
Since the equation represents a line, there are three possible scenarios for the number of solutions:
1. The line intersects the x-axis and y-axis at a single point. This would mean that the equation has a unique solution.
2. The line is parallel to the x-axis and does not intersect the y-axis. This would mean that the equation has no solution.
3. The line is neither parallel to the x-axis nor the y-axis. This would mean that the equation has infinitely many solutions.
In this case, the line has a slope of -2/5, so it is not parallel to the x-axis or the y-axis. Therefore, the equation has infinitely many solutions.
The given linear equation is 2x + 5y = 8. To determine the number of solutions, we can convert this equation into slope-intercept form.
2x + 5y = 8
5y = -2x + 8
y = (-2/5)x + 8/5
Now we can see that the equation has a slope of -2/5 and a y-intercept of 8/5. This means that the equation represents a line in the coordinate plane.
Infinitely many solutions:
Since the equation represents a line, there are three possible scenarios for the number of solutions:
1. The line intersects the x-axis and y-axis at a single point. This would mean that the equation has a unique solution.
2. The line is parallel to the x-axis and does not intersect the y-axis. This would mean that the equation has no solution.
3. The line is neither parallel to the x-axis nor the y-axis. This would mean that the equation has infinitely many solutions.
In this case, the line has a slope of -2/5, so it is not parallel to the x-axis or the y-axis. Therefore, the equation has infinitely many solutions.
All linear equations in two variables have ————– .- a)One solution
- b)Infinitely many solutions
- c)Three solutions
- d)Two solution
Correct answer is option 'B'. Can you explain this answer?
All linear equations in two variables have ————– .
a)
One solution
b)
Infinitely many solutions
c)
Three solutions
d)
Two solution
|
Khushi answered |
In a linear equation in two variables,for every value of x there exists another value for y. so there are infinite solutions that is why option B is correct . UPvote if that helps :)
- a)3rd quadrant
- b)Ist quadrant
- c)4th quadrant
- d)2nd quadrant
Correct answer is 'B'. Can you explain this answer?
|
|
Arjun Sharma answered |
The solution of the linear equation is represented by the ordered pair (x, y).If x > 0, y > 0, then solution lies in first quadrant.
Which of the following points lies on the line 3x + 2y = 6?- a)(1, 2)
- b)(3, 0)
- c)(2, 3)
- d)(0, 3)
Correct answer is option 'D'. Can you explain this answer?
Which of the following points lies on the line 3x + 2y = 6?
a)
(1, 2)
b)
(3, 0)
c)
(2, 3)
d)
(0, 3)
|
|
Anita Menon answered |
Put the given points in the equation 3x + 2y = 6
If L.H.S of the equation is equal to R.H.S
then the given points will lie on the line
3x + 2y = 6
3.0 + 2.3 = 6
6 =6
L.H.S = R.H.S
So the given point lie on the line.
Which of the following is not the solution of linear equation 
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
Which of the following is not the solution of linear equation
a)
b)
c)
d)
|
User3820317 answered |
Answer will be a.} 0,√2
because 0+√2=√2
because 0+√2=√2
——————- is the equation of y-axis.- a)y = 1
- b)x = 0
- c)y = -1
- d)y = 0
Correct answer is option 'B'. Can you explain this answer?
——————- is the equation of y-axis.
a)
y = 1
b)
x = 0
c)
y = -1
d)
y = 0
|
Preetam Pyare answered |
Since Every Equation lies on y-axis AtQ.. So, 'x' coordinate of eqn. might be 0 and 'y' Coordinate can be any integer.so,x=0 is the equation of y-axis.Hence,Option(B) is d correct answer..
The force applied on a body is directly proportional to the acceleration produced in the body. Assume x be acceleration produced in the body and y be the force. Take constant as 10.(S.I unit of force is Newton and S.I. unit of acceleration is m/sec2.
Q. Find acceleration produced in the body, if force applied is 10 newtons.- a)1 m/sec2
- b)2 m/sec2
- c)3 m/sec2
- d)4 m/sec2
Correct answer is option 'A'. Can you explain this answer?
The force applied on a body is directly proportional to the acceleration produced in the body. Assume x be acceleration produced in the body and y be the force. Take constant as 10.(S.I unit of force is Newton and S.I. unit of acceleration is m/sec2.
Q. Find acceleration produced in the body, if force applied is 10 newtons.
a)
1 m/sec2
b)
2 m/sec2
c)
3 m/sec2
d)
4 m/sec2
|
|
Anita Menon answered |
Given,
Force applied = 10 newtons
c = 10
Since, y = cx
⇒ 10 = 10x
⇒ x = 1
Thus, acceleration produced = 1 m/sec2
A linear equation in one variable is an equation of the form ………..- a)ax + b = 0, where a, b , c are real numbers
- b)ax = c, where a and c are real numbers
- c)by = c, where band c are real number
- d)All of above
Correct answer is option 'D'. Can you explain this answer?
A linear equation in one variable is an equation of the form ………..
a)
ax + b = 0, where a, b , c are real numbers
b)
ax = c, where a and c are real numbers
c)
by = c, where band c are real number
d)
All of above
|
Preethi Singh answered |
A linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1. Linear equations in one variable may take the form a x + b = 0, ax+b=0, ax+b=0 and are solved using basic algebraic operations
Temperature is a measure of the warmth or coldness of an object or substance with reference to some standard value.In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius.An equation that converts Fahrenheit to Celsius is:
On reading the above information, some queries come in Aman’s mind. Help him to resolve his following queries:Answer the following :Q. What is a temperature which is numerically the same in both Fahrenheit and Celsius ?- a)40
- b)– 40
- c)30
- d)– 20
Correct answer is option 'B'. Can you explain this answer?
Temperature is a measure of the warmth or coldness of an object or substance with reference to some standard value.
In countries like USA and Canada, temperature is measured in Fahrenheit, whereas in countries like India, it is measured in Celsius.
An equation that converts Fahrenheit to Celsius is:
On reading the above information, some queries come in Aman’s mind. Help him to resolve his following queries:
Answer the following :
Q. What is a temperature which is numerically the same in both Fahrenheit and Celsius ?
a)
40
b)
– 40
c)
30
d)
– 20
|
|
Swati Verma answered |
5x = 9x + 160
5x – 9x = 160
– 4x = 160
x = – 40
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion: x + y = 3 is the equation of a line passing through the origin.Reason: y = 2x is the equation of a line passing through the origin.- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'D'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: x + y = 3 is the equation of a line passing through the origin.
Reason: y = 2x is the equation of a line passing through the origin.
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
|
Rohit Sharma answered |
For Assertion: The given linear equation is x + y = 3
Since x = 0 and y = 0 is not satisfying x + y = 3, therefore it is not passing through the origin.
So, Assertion is not correct.
Since x = 0 and y = 0 is not satisfying y = 2x, therefore it is passing through the origin.
So, Reason is correct. Correct option is (d) Assertion (A) is false but reason (R) is true.
2x + 4 = 3x + 1 will represent a.- a)Line parallel to X-axis at distance 3 units upwards
- b)Line parallel to X-axis at distance 3 units downwards
- c)Line parallel to Y-axis at distance 3 units left side
- d)Line parallel to Y-axis at distance 3 units on right side
Correct answer is option 'D'. Can you explain this answer?
2x + 4 = 3x + 1 will represent a.
a)
Line parallel to X-axis at distance 3 units upwards
b)
Line parallel to X-axis at distance 3 units downwards
c)
Line parallel to Y-axis at distance 3 units left side
d)
Line parallel to Y-axis at distance 3 units on right side
|
|
Anika Reddy answered |
Solution:
Given equation is 2x - 4 = 3x - 1.
To find the line parallel to the Y-axis at a distance of 3 units on the right side, we need to first solve the given equation for x.
2x - 4 = 3x - 1
Subtracting 2x from both sides, we get
-4 = x - 1
Adding 1 to both sides, we get
-3 = x
Therefore, the value of x is -3.
To find the line parallel to the Y-axis at a distance of 3 units on the right side, we need to draw a vertical line passing through x = -3 and then shift it 3 units to the right.
Hence, the correct option is D - Line parallel to Y-axis at a distance of 3 units on the right side.
HTML Representation:
Solution:
Given equation: 2x - 4 = 3x - 1.
To find the line parallel to the Y-axis at a distance of 3 units on the right side, we need to first solve the given equation for x.
2x - 4 = 3x - 1
Subtracting 2x from both sides, we get
-4 = x - 1
Adding 1 to both sides, we get
-3 = x
Therefore, the value of x is -3.
To find the line parallel to the Y-axis at a distance of 3 units on the right side, we need to draw a vertical line passing through x = -3 and then shift it 3 units to the right.
Hence, the correct option is D - Line parallel to Y-axis at a distance of 3 units on the right side.
Given equation is 2x - 4 = 3x - 1.
To find the line parallel to the Y-axis at a distance of 3 units on the right side, we need to first solve the given equation for x.
2x - 4 = 3x - 1
Subtracting 2x from both sides, we get
-4 = x - 1
Adding 1 to both sides, we get
-3 = x
Therefore, the value of x is -3.
To find the line parallel to the Y-axis at a distance of 3 units on the right side, we need to draw a vertical line passing through x = -3 and then shift it 3 units to the right.
Hence, the correct option is D - Line parallel to Y-axis at a distance of 3 units on the right side.
HTML Representation:
Solution:
Given equation: 2x - 4 = 3x - 1.
To find the line parallel to the Y-axis at a distance of 3 units on the right side, we need to first solve the given equation for x.
2x - 4 = 3x - 1
Subtracting 2x from both sides, we get
-4 = x - 1
Adding 1 to both sides, we get
-3 = x
Therefore, the value of x is -3.
To find the line parallel to the Y-axis at a distance of 3 units on the right side, we need to draw a vertical line passing through x = -3 and then shift it 3 units to the right.
Hence, the correct option is D - Line parallel to Y-axis at a distance of 3 units on the right side.
The cost of a pencil is thrice the cost of rubber.The equivalent linear equation in two variables of above statement is:- a)p = 3 -r
- b)p =1/3 +r
- c)p = 3r
- d)p = 3 + r
Correct answer is option 'C'. Can you explain this answer?
The cost of a pencil is thrice the cost of rubber.The equivalent linear equation in two variables of above statement is:
a)
p = 3 -r
b)
p =1/3 +r
c)
p = 3r
d)
p = 3 + r
|
|
Krithika Sen answered |
Explanation:
Let the cost of rubber be 'r' and the cost of pencil be 'p'.
The given statement states that:
The cost of a pencil is thrice the cost of rubber.
This can be written as:
p = 3r
This is the required linear equation in two variables.
Option Analysis:
a) p = 3 - r
This equation is not equivalent to the given statement. It states that the cost of pencil is equal to 3 minus the cost of rubber, which is not the same as stating that the cost of pencil is thrice the cost of rubber.
b) p = 1/3r
This equation is also not equivalent to the given statement. It states that the cost of pencil is equal to one-third of the cost of rubber, which is not the same as stating that the cost of pencil is thrice the cost of rubber.
c) p = 3r
This equation is the correct equivalent linear equation in two variables of the given statement.
d) p = 3 r
This equation is not equivalent to the given statement. It states that the cost of pencil is equal to 3 and the cost of rubber is equal to 'r', which is not the same as stating that the cost of pencil is thrice the cost of rubber.
Therefore, the correct option is (c) p = 3r.
Let the cost of rubber be 'r' and the cost of pencil be 'p'.
The given statement states that:
The cost of a pencil is thrice the cost of rubber.
This can be written as:
p = 3r
This is the required linear equation in two variables.
Option Analysis:
a) p = 3 - r
This equation is not equivalent to the given statement. It states that the cost of pencil is equal to 3 minus the cost of rubber, which is not the same as stating that the cost of pencil is thrice the cost of rubber.
b) p = 1/3r
This equation is also not equivalent to the given statement. It states that the cost of pencil is equal to one-third of the cost of rubber, which is not the same as stating that the cost of pencil is thrice the cost of rubber.
c) p = 3r
This equation is the correct equivalent linear equation in two variables of the given statement.
d) p = 3 r
This equation is not equivalent to the given statement. It states that the cost of pencil is equal to 3 and the cost of rubber is equal to 'r', which is not the same as stating that the cost of pencil is thrice the cost of rubber.
Therefore, the correct option is (c) p = 3r.
Prime Minister ’s National Relief Fund (also called PMNRF in short) is the fund raised to provide support for people affected by natural and manmade disasters. Natural disasters that are covered under this include flood, cyclone, earthquake etc. Man-made disasters that are included are major accidents, acid attacks, riots, etc.
Two friends Sita and Gita, together contributed ₹ 200 towards Prime Minister’s Relief Fund. Answer the following :Q. If both contributed equally, then how much is contributed by each?- a)₹ 50, ₹ 150
- b)₹ 100, ₹ 100
- c)₹ 50, ₹ 50
- d)₹ 120, ₹ 120
Correct answer is option 'B'. Can you explain this answer?
Prime Minister ’s National Relief Fund (also called PMNRF in short) is the fund raised to provide support for people affected by natural and manmade disasters. Natural disasters that are covered under this include flood, cyclone, earthquake etc. Man-made disasters that are included are major accidents, acid attacks, riots, etc.
Two friends Sita and Gita, together contributed ₹ 200 towards Prime Minister’s Relief Fund. Answer the following :
Q. If both contributed equally, then how much is contributed by each?
a)
₹ 50, ₹ 150
b)
₹ 100, ₹ 100
c)
₹ 50, ₹ 50
d)
₹ 120, ₹ 120
|
Meera Rana answered |
If x = y then x + x = 200
2x = 200
Thus, each contributed is ₹ 100.
Point P(2,-3) lies on the line represented by the equation:- a)x + 2y = 0
- b)x + y = 1
- c)2x + y = 1
- d)2x + 2y = 0
Correct answer is option 'C'. Can you explain this answer?
Point P(2,-3) lies on the line represented by the equation:
a)
x + 2y = 0
b)
x + y = 1
c)
2x + y = 1
d)
2x + 2y = 0
|
Shubham Iyer answered |
Solution:
To check which equation represents the line passing through point P(2,-3), we need to substitute the coordinates of P into each equation and see which one satisfies the equation.
Let's check each option one by one:
a) x + 2y = 0
Substituting (2,-3) into this equation:
2 + 2(-3) = -4
The point (2,-3) does not satisfy the equation, so this is not the correct option.
b) x + y = 1
Substituting (2,-3) into this equation:
2 + (-3) = -1
The point (2,-3) does not satisfy the equation, so this is not the correct option.
c) 2x + y = 1
Substituting (2,-3) into this equation:
2(2) + (-3) = 1
The point (2,-3) satisfies the equation, so this is the correct option.
d) 2x + 2y = 0
Substituting (2,-3) into this equation:
2(2) + 2(-3) = -2
The point (2,-3) does not satisfy the equation, so this is not the correct option.
Therefore, the equation that represents the line passing through point P(2,-3) is 2x + y = 1, option C.
To check which equation represents the line passing through point P(2,-3), we need to substitute the coordinates of P into each equation and see which one satisfies the equation.
Let's check each option one by one:
a) x + 2y = 0
Substituting (2,-3) into this equation:
2 + 2(-3) = -4
The point (2,-3) does not satisfy the equation, so this is not the correct option.
b) x + y = 1
Substituting (2,-3) into this equation:
2 + (-3) = -1
The point (2,-3) does not satisfy the equation, so this is not the correct option.
c) 2x + y = 1
Substituting (2,-3) into this equation:
2(2) + (-3) = 1
The point (2,-3) satisfies the equation, so this is the correct option.
d) 2x + 2y = 0
Substituting (2,-3) into this equation:
2(2) + 2(-3) = -2
The point (2,-3) does not satisfy the equation, so this is not the correct option.
Therefore, the equation that represents the line passing through point P(2,-3) is 2x + y = 1, option C.
The number of girls x in a class is 5 less than twice the number of boys y of the same class. The linear equation in two variables for this information is- a)x + 5 = 2y
- b)2x – y = 5
- c)2y – x = -5
- d)x + 2y = -5
Correct answer is option 'A'. Can you explain this answer?
The number of girls x in a class is 5 less than twice the number of boys y of the same class. The linear equation in two variables for this information is
a)
x + 5 = 2y
b)
2x – y = 5
c)
2y – x = -5
d)
x + 2y = -5
|
|
Gautam answered |
The girls are x and boys are y
we will get the equation
x=2y-5 from the given information
which is nothing but
x+5=2y
we will get the equation
x=2y-5 from the given information
which is nothing but
x+5=2y
Which of the following pairs is a solution to the equation 4x + 3y = 10?- a)(1, 2)
- b)(0, 4)
- c)(-1, 6)
- d)(2, 0)
Correct answer is option 'A'. Can you explain this answer?
Which of the following pairs is a solution to the equation 4x + 3y = 10?
a)
(1, 2)
b)
(0, 4)
c)
(-1, 6)
d)
(2, 0)
|
|
Let's Tute answered |
To find which pair is a solution to the equation 4x + 3y = 10, substitute each pair into the equation:
(1, 2): Substitute to get
This pair works.
4(1)+3(2)
= 4+6
= 10.This pair works.
(0, 4): Substitute to get
This pair does not work.
4(0)+3(4)
= 0+12
= 12.This pair does not work.
(-1, 6): Substitute to get
This pair does not work.
4(-1)+3(6)
= -4+18
= 14.This pair does not work.
(2, 0): Substitute to get
This pair does not work.
4(2)+3(0)
= 8+0
= 8.This pair does not work.
The solution is (1, 2) because it satisfies the equation.
If x=2 and y=1 is a solution of the equation 2x+3y=k, what is the value of k?- a)8
- b)7
- c)6
- d)5
Correct answer is option 'B'. Can you explain this answer?
If x=2 and y=1 is a solution of the equation 2x+3y=k, what is the value of k?
a)
8
b)
7
c)
6
d)
5
|
|
Let's Tute answered |
Substituting x = 2 and y = 1 into the equation:
2(2) + 3(1) = 4 + 3 = 7, so k = 7.
2(2) + 3(1) = 4 + 3 = 7, so k = 7.
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:Assertion : If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, then the value of k is 10Reason : A linear equation in two variables has infinitely many solutions.- a)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
- b)Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
- c)Assertion (A) is true but reason (R) is false.
- d)Assertion (A) is false but reason (R) is true.
Correct answer is option 'B'. Can you explain this answer?
DIRECTION : In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion : If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, then the value of k is 10
Reason : A linear equation in two variables has infinitely many solutions.
a)
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
b)
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
c)
Assertion (A) is true but reason (R) is false.
d)
Assertion (A) is false but reason (R) is true.
|
|
Swati Verma answered |
We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.
Since x = 2k -1 and y = k is solution of the given linear equation, we have 3 x (2k -1) -5k -7 = 0 ⇒ 6k -3 -5k -7 = 0 ⇒ k -10 = 0 ⇒ k = 10.
So, Assertion is also correct
But reason (R) is not the correct explanation of assertion (A).
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
Which of the following is a solution to the equation x=4?- a)(1, 4)
- b)(2, 3)
- c)(3, 4)
- d)(4, 1)
Correct answer is option 'D'. Can you explain this answer?
Which of the following is a solution to the equation x=4?
a)
(1, 4)
b)
(2, 3)
c)
(3, 4)
d)
(4, 1)
|
|
Madhurima Ahuja answered |
Understanding the Equation x = 4
The equation x = 4 indicates that the value of x is fixed at 4. This means that any point that is a solution to this equation must have its x-coordinate equal to 4.
Evaluating the Options
Let’s analyze each option to determine which one satisfies the equation:
Conclusion
The correct answer is option 'D', (4, 1), because it is the only point among the given options where the x-coordinate matches the value specified in the equation x = 4. Thus, it satisfies the condition set by the equation.
The equation x = 4 indicates that the value of x is fixed at 4. This means that any point that is a solution to this equation must have its x-coordinate equal to 4.
Evaluating the Options
Let’s analyze each option to determine which one satisfies the equation:
- a) (1, 4)
- Here, the x-coordinate is 1.
- Since 1 is not equal to 4, this point is NOT a solution. - b) (2, 3)
- Here, the x-coordinate is 2.
- Since 2 is not equal to 4, this point is NOT a solution. - c) (3, 4)
- Here, the x-coordinate is 3.
- Since 3 is not equal to 4, this point is NOT a solution. - d) (4, 1)
- Here, the x-coordinate is 4.
- Since 4 is equal to 4, this point IS a solution.
Conclusion
The correct answer is option 'D', (4, 1), because it is the only point among the given options where the x-coordinate matches the value specified in the equation x = 4. Thus, it satisfies the condition set by the equation.
The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is- a)7
- b)-7
- c)6
- d)5
Correct answer is option 'A'. Can you explain this answer?
The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is
a)
7
b)
-7
c)
6
d)
5
|
Granger answered |
2*2-k=-3*1(by putting the value of X and y)
4-k=-3
4+3=k
k=7
4-k=-3
4+3=k
k=7
The force applied on a body is directly proportional to the acceleration produced in the body. Assume x be acceleration produced in the body and y be the force. Take constant as 10.(S.I unit of force is Newton and S.I. unit of acceleration is m/sec2.
Q. Name the type of equation formed in part(A).- a)Quadratic equation
- b)Cubic equation
- c)Zero equation
- d)Linear equation
Correct answer is option 'D'. Can you explain this answer?
The force applied on a body is directly proportional to the acceleration produced in the body. Assume x be acceleration produced in the body and y be the force. Take constant as 10.(S.I unit of force is Newton and S.I. unit of acceleration is m/sec2.
Q. Name the type of equation formed in part(A).
a)
Quadratic equation
b)
Cubic equation
c)
Zero equation
d)
Linear equation
|
|
Amit Sharma answered |
Y = cx is a linear equation as highest power of x is 1.
Solutions of the equation 2x + 5y = 0 is:- a)3,0
- b)-3,2
- c)0,0
- d)0,4
Correct answer is option 'C'. Can you explain this answer?
Solutions of the equation 2x + 5y = 0 is:
a)
3,0
b)
-3,2
c)
0,0
d)
0,4
|
|
Prateek Kushwaha answered |
Put the value of x and y
if we put
x=0
y=0..
2×0+5×0=0
otherwise
if we try other option so you don't get equal 0
if we put
x=0
y=0..
2×0+5×0=0
otherwise
if we try other option so you don't get equal 0
Difference between the cost of a carpet(C) and a durries(D) is Rs.200. If the carpet is the costlier one of the two, which of the following represents this information?a)C – D = 200b)C – D = 100c)D – C = 200d)C + D = 200Correct answer is option 'A'. Can you explain this answer?
|
Arya Desai answered |
Given,
diff. between the cost of carpet c and durries d is 200,the carpet is costlier
NOW,
c - d = 200
c = 200+d
diff. between the cost of carpet c and durries d is 200,the carpet is costlier
NOW,
c - d = 200
c = 200+d
Which equation represents the relationship where x + 2y = 6 ?- a)x − 2y + 6 = 0
- b)x + 2y − 6= 0
- c)x − 2y − 6 = 0
- d)x + 2y + 6 = 0
Correct answer is option 'B'. Can you explain this answer?
Which equation represents the relationship where x + 2y = 6 ?
a)
x − 2y + 6 = 0
b)
x + 2y − 6= 0
c)
x − 2y − 6 = 0
d)
x + 2y + 6 = 0
|
Hridoy Nair answered |
Understanding the Equation
The equation given is x + 2y = 6. This is a linear equation in two variables, x and y. The goal is to rearrange this equation to match the options provided.
Rearranging the Equation
To rewrite the equation in the standard form (Ax + By + C = 0), we can manipulate the original equation:
- Start with x + 2y = 6.
- Subtract 6 from both sides to bring all terms to one side:
x + 2y - 6 = 0.
This matches the standard form Ax + By + C = 0 where A = 1, B = 2, and C = -6.
Matching with Options
Now, let’s compare the rearranged equation with the provided options:
- a) x - 2y + 6 = 0
- b) x + 2y - 6 = 0
- c) x - 2y - 6 = 0
- d) x + 2y + 6 = 0
The rearranged equation x + 2y - 6 = 0 corresponds exactly with option b.
Conclusion
Thus, the correct answer is option 'B': x + 2y - 6 = 0. This form clearly shows the relationship defined by the original equation.
The equation given is x + 2y = 6. This is a linear equation in two variables, x and y. The goal is to rearrange this equation to match the options provided.
Rearranging the Equation
To rewrite the equation in the standard form (Ax + By + C = 0), we can manipulate the original equation:
- Start with x + 2y = 6.
- Subtract 6 from both sides to bring all terms to one side:
x + 2y - 6 = 0.
This matches the standard form Ax + By + C = 0 where A = 1, B = 2, and C = -6.
Matching with Options
Now, let’s compare the rearranged equation with the provided options:
- a) x - 2y + 6 = 0
- b) x + 2y - 6 = 0
- c) x - 2y - 6 = 0
- d) x + 2y + 6 = 0
The rearranged equation x + 2y - 6 = 0 corresponds exactly with option b.
Conclusion
Thus, the correct answer is option 'B': x + 2y - 6 = 0. This form clearly shows the relationship defined by the original equation.
Which of the following pair is a solution of the equation 3x – 2y = 7?- a)(1, -2)
- b)(-2, 1)
- c)(5, 1)
- d)(1, 5)
Correct answer is option 'A'. Can you explain this answer?
Which of the following pair is a solution of the equation 3x – 2y = 7?
a)
(1, -2)
b)
(-2, 1)
c)
(5, 1)
d)
(1, 5)
|
Rhea Dey answered |
Understanding the Equation
To determine which pair is a solution to the equation 3x - 2y = 7, we need to substitute each pair (x, y) into the equation and check if it holds true.
Evaluating the Options
Here are the given pairs:
Substituting Each Pair
1. Option a: (1, -2)
- Substitute x = 1 and y = -2 into the equation:
- 3(1) - 2(-2) = 3 + 4 = 7
- This is correct, so (1, -2) is a solution.
2. Option b: (-2, 1)
- Substitute x = -2 and y = 1:
- 3(-2) - 2(1) = -6 - 2 = -8
- This is not equal to 7, so (-2, 1) is not a solution.
3. Option c: (5, 1)
- Substitute x = 5 and y = 1:
- 3(5) - 2(1) = 15 - 2 = 13
- This is not equal to 7, so (5, 1) is not a solution.
4. Option d: (1, 5)
- Substitute x = 1 and y = 5:
- 3(1) - 2(5) = 3 - 10 = -7
- This is not equal to 7, so (1, 5) is not a solution.
Conclusion
After evaluating all options, the only correct solution is:
Option a: (1, -2)
This confirms that the pair (1, -2) satisfies the equation 3x - 2y = 7.
To determine which pair is a solution to the equation 3x - 2y = 7, we need to substitute each pair (x, y) into the equation and check if it holds true.
Evaluating the Options
Here are the given pairs:
- a) (1, -2)
- b) (-2, 1)
- c) (5, 1)
- d) (1, 5)
Substituting Each Pair
1. Option a: (1, -2)
- Substitute x = 1 and y = -2 into the equation:
- 3(1) - 2(-2) = 3 + 4 = 7
- This is correct, so (1, -2) is a solution.
2. Option b: (-2, 1)
- Substitute x = -2 and y = 1:
- 3(-2) - 2(1) = -6 - 2 = -8
- This is not equal to 7, so (-2, 1) is not a solution.
3. Option c: (5, 1)
- Substitute x = 5 and y = 1:
- 3(5) - 2(1) = 15 - 2 = 13
- This is not equal to 7, so (5, 1) is not a solution.
4. Option d: (1, 5)
- Substitute x = 1 and y = 5:
- 3(1) - 2(5) = 3 - 10 = -7
- This is not equal to 7, so (1, 5) is not a solution.
Conclusion
After evaluating all options, the only correct solution is:
Option a: (1, -2)
This confirms that the pair (1, -2) satisfies the equation 3x - 2y = 7.
Which of the following is a solution to the equation 2x+y=7?- a)(1, 4)
- b)(2, 3)
- c)(3, 2)
- d)(4, 1)
Correct answer is option 'B'. Can you explain this answer?
Which of the following is a solution to the equation 2x+y=7?
a)
(1, 4)
b)
(2, 3)
c)
(3, 2)
d)
(4, 1)
|
|
Let's Tute answered |
Correct Answer: B - (2,3)
x = 2 and y = 3into the equation:
2(2) + 3 = 4 + 3 = 7, which is true.
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