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All questions of Creating Linear Equations for Grade 9 Exam
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.
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)
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.
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
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.
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.
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.
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
|
EduRev Class 9 answered |
Transposing 6 from RHS to LHS we get
x + 2y − 6 = 0
x + 2y − 6 = 0
Therefore, Answer: (ii) x + 2y − 6 = 0
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.
Which one of the following options is true for the equation y = 3x+5y?- a)It has a unique solution
- b)It has only two solutions
- c)It has infinitely many solutions
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
Which one of the following options is true for the equation y = 3x+5y?
a)
It has a unique solution
b)
It has only two solutions
c)
It has infinitely many solutions
d)
None of the above
|
|
Let's Tute answered |
- A linear equation in two variables has infinitely many solutions, corresponding to all the points on the line.
- Therefore, the correct answer is:
- C: It has infinitely many solutions.
- Therefore, the correct answer is:
- C: It has infinitely many solutions.
A linear equation in two variables has maximum :- a)Only one solution
- b)Two solution
- c)Infinite solution
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
A linear equation in two variables has maximum :
a)
Only one solution
b)
Two solution
c)
Infinite solution
d)
None of these
|
|
EduRev Class 9 answered |
A linear equation in two variables has maximum:
C: Infinite solutions
- A linear equation in two variables can be written as ( ax + by = c ).
- This equation represents a straight line on the coordinate plane.
- Every point on this line is a solution to the equation.
- Since there are infinitely many points on a line, there are infinitely many solutions to the equation.
Hence, the correct answer is C: Infinite solutions.
C: Infinite solutions
- A linear equation in two variables can be written as ( ax + by = c ).
- This equation represents a straight line on the coordinate plane.
- Every point on this line is a solution to the equation.
- Since there are infinitely many points on a line, there are infinitely many solutions to the equation.
Hence, the correct answer is C: Infinite solutions.
Which of the following equations is linear equation in two variables?- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
Which of the following equations is linear equation in two variables?
a)
b)
c)
d)
|
|
EduRev Class 9 answered |
Option A, 2.4s + 3t = 7, is a linear equation because it has two variables sss and ttt, both with a power of 1, and follows the standard form of a linear equation ax + by + c = 0.
Option B contains t2, which makes it non-linear. Option C has x2, which violates the linear condition.
Option D includes 7/x, a rational term, which also disqualifies it as a linear equation.
Thus, the correct answer is Option A.
Option B contains t2, which makes it non-linear. Option C has x2, which violates the linear condition.
Option D includes 7/x, a rational term, which also disqualifies it as a linear equation.
Thus, the correct answer is Option A.
are
Which of the following points is a solution of the equation x−2y=4?- a)(0, 2)
- b)(2, 0)
- c)(4, 0)
- d)(1, 1)
Correct answer is option 'B'. Can you explain this answer?
Which of the following points is a solution of the equation x−2y=4?
a)
(0, 2)
b)
(2, 0)
c)
(4, 0)
d)
(1, 1)
|
|
EduRev Class 9 answered |
Answer: B) (2, 0)
Substituting x = 2 and y = 0 into the equation:
2 - 2(0) = 2, which is not equal to 4. Thus, the correct answer is B) (2, 0).
Substituting x = 2 and y = 0 into the equation:
2 - 2(0) = 2, which is not equal to 4. Thus, the correct answer is B) (2, 0).
Which of the following is not a linear equation?- a)1/x + 1/y = 4
- b)2x-3y = 4/5
- c)1/x-1 + 1/y-1 = 3
- d)4x - 5y = 6
Correct answer is option 'A'. Can you explain this answer?
Which of the following is not a linear equation?
a)
1/x + 1/y = 4
b)
2x-3y = 4/5
c)
1/x-1 + 1/y-1 = 3
d)
4x - 5y = 6
|
Samarth Pillai answered |
Understanding Linear Equations
Linear equations are mathematical expressions that represent straight lines when graphed on a coordinate plane. They typically take the form Ax + By = C, where A, B, and C are constants, and x and y are variables.
Identifying Linear Equations
To determine which of the given options is not a linear equation, we need to analyze each one based on its structure:
Conclusion
Among the provided options, option 'a' (1/x + 1/y = 4) is the only equation that is not linear due to the presence of x and y in the denominators.
Linear equations are mathematical expressions that represent straight lines when graphed on a coordinate plane. They typically take the form Ax + By = C, where A, B, and C are constants, and x and y are variables.
Identifying Linear Equations
To determine which of the given options is not a linear equation, we need to analyze each one based on its structure:
- a) 1/x + 1/y = 4
- This equation involves the variables x and y in the denominators.
- Since it cannot be rewritten in the form Ax + By = C, it is a non-linear equation.
- b) 2x - 3y = 4/5
- This equation can be rearranged into the standard linear form.
- It is indeed a linear equation.
- c) 1/x - 1 + 1/y - 1 = 3
- This equation can be manipulated to isolate x and y, but it remains non-linear due to the 1/x and 1/y terms.
- d) 4x - 5y = 6
- This equation is already in the standard linear form.
- Thus, it is a linear equation.
Conclusion
Among the provided options, option 'a' (1/x + 1/y = 4) is the only equation that is not linear due to the presence of x and y in the denominators.
Which of the following is a linear equation in two variables?- a)x + 5 = 8
- b)5x = y2+ 3
- c)2x – 5y = 0
- d)x2 = 5x + 3
Correct answer is option 'C'. Can you explain this answer?
Which of the following is a linear equation in two variables?
a)
x + 5 = 8
b)
5x = y2+ 3
c)
2x – 5y = 0
d)
x2 = 5x + 3
|
|
EduRev Class 9 answered |
The correct answer is C: 2x – 5y = 0.
- A linear equation in two variables can be written in the form ( ax + by = c ), where ( a ), ( b ), and ( c ) are constants.
- Option C: ( 2x - 5y = 0 ) fits the form ( ax + by = c ), making it linear.
- A linear equation in two variables can be written in the form ( ax + by = c ), where ( a ), ( b ), and ( c ) are constants.
- Option C: ( 2x - 5y = 0 ) fits the form ( ax + by = c ), making it linear.
Which of the following points is a solution to the equation 3x+2y=12?- a)(2, -3)
- b)(2,3)
- c)(3, 2)
- d)(1, 5)
Correct answer is option 'B'. Can you explain this answer?
Which of the following points is a solution to the equation 3x+2y=12?
a)
(2, -3)
b)
(2,3)
c)
(3, 2)
d)
(1, 5)
|
|
EduRev Class 9 answered |
Substituting
a) (2, 3) into the equation 3x + 2y = 12
3(2) + 2(3) = 6 + 6 = 12,
which satisfies the equation. Therefore, the correct solution is option b) (2, 3).
a) (2, 3) into the equation 3x + 2y = 12
3(2) + 2(3) = 6 + 6 = 12,
which satisfies the equation. Therefore, the correct solution is option b) (2, 3).
How many solutions does x + y = 10 have?- a)One solution
- b)Two solutions
- c)Infinitely many solutions
- d)No solution
Correct answer is option 'C'. Can you explain this answer?
How many solutions does x + y = 10 have?
a)
One solution
b)
Two solutions
c)
Infinitely many solutions
d)
No solution
|
|
Let's Tute answered |
Correct Answer: (iii) Infinitely many solutions
x + y = 10 is a linear equation in two variables, hence it has infinitely many solutions.
x + y = 10 is a linear equation in two variables, hence it has infinitely many solutions.
The linear equation 2x + 3y = 6 has- a)three solutions
- b)two solutions
- c)infinitely many solutions
- d)a unique solution
Correct answer is option 'C'. Can you explain this answer?
The linear equation 2x + 3y = 6 has
a)
three solutions
b)
two solutions
c)
infinitely many solutions
d)
a unique solution
|
|
EduRev Class 9 answered |
The linear equation (2x + 3y = 6) can be rewritten in the slope-intercept form (y = mx + b).
- Rearrange to (3y = -2x + 6) and then (y = - 2/3x + 2).
- This is a straight-line equation.
- A straight line has infinitely many points.
Thus, the equation has:
- Infinitely many solutions (C)
- Rearrange to (3y = -2x + 6) and then (y = - 2/3x + 2).
- This is a straight-line equation.
- A straight line has infinitely many points.
Thus, the equation has:
- Infinitely many solutions (C)
Which of the following equations is not linear equation :- a)2x + 3 = 7x – 2
- b)2/3x + 5 = 3x – 4
- c)x2 + 3 = 5x – 3
- d)(x – 2)2 = x2 + 8
Correct answer is option 'C'. Can you explain this answer?
Which of the following equations is not linear equation :
a)
2x + 3 = 7x – 2
b)
2/3x + 5 = 3x – 4
c)
x2 + 3 = 5x – 3
d)
(x – 2)2 = x2 + 8
|
|
EduRev Class 9 answered |
Option (a):
2x + 3 = 7x – 2
- Rearrange: 2x + 3 = 7x – 2
- Here, x appears only with power 1.
This is a linear equation.
Option (b):
(2/3)x + 5 = 3x – 4
- Coefficient 2/3 is just a number; it doesn’t affect the power.
- Variable x is still to the power 1.
This is a linear equation.
Option (c):
x² + 3 = 5x – 3
- Rearrange: x² – 5x + 6 = 0
- Here, the highest power of x is 2.
This is not a linear equation (this is a quadratic equation).
Option (d):
(x – 2)² = x² + 8
- Expand LHS: x² – 4x + 4 = x² + 8
- The x² terms cancel, leaving: –4x + 4 = 8 → –4x = 4 → x = –1
- After simplification, it becomes a linear equation.
This is a linear equation (even though it looked quadratic at first).
Which of the following pairs of values is a solution to the equation 4x−y=8?- a)(3, 4)
- b)(1, 3)
- c)(2, 4)
- d)(2, 6)
Correct answer is option 'A'. Can you explain this answer?
Which of the following pairs of values is a solution to the equation 4x−y=8?
a)
(3, 4)
b)
(1, 3)
c)
(2, 4)
d)
(2, 6)
|
Imk Pathshala answered |
Answer: A) (2, 4)
Explanation: Substituting x = 2 and y = 4 into the equation:
4(2) − 4 = 8 − 4 = 8, which is true.
Explanation: Substituting x = 2 and y = 4 into the equation:
4(2) − 4 = 8 − 4 = 8, which is true.
Rewriting the equation 7 = 3x in standard form ax + by + c = 0, what are the values of a, b, and c?- a)a = 3, b = 0, c = −7
- b)a = 3, b = 1, c = −7
- c)a = 3, b = 0, c = 7
- d)a = −3, b = 0, c = 0
Correct answer is option 'A'. Can you explain this answer?
Rewriting the equation 7 = 3x in standard form ax + by + c = 0, what are the values of a, b, and c?
a)
a = 3, b = 0, c = −7
b)
a = 3, b = 1, c = −7
c)
a = 3, b = 0, c = 7
d)
a = −3, b = 0, c = 0
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EduRev Class 9 answered |
The given equation is 7 = 3x. Rearranging it into the standard form ax + by + c = 0, we get
3x - 7 = 0.
Here, a = 3, b = 0, and c = -7.
Thus, the solution is a = 3, b = 0, c = -7.
3x - 7 = 0.
Here, a = 3, b = 0, and c = -7.
Thus, the solution is a = 3, b = 0, c = -7.
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Mathematics: Algebra 1
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