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All questions of Pair of Linear Equations in Two Variables for Class 10 Exam
A pair of linear equations which has a unique solution x = 2, y = - 3 is
- a)x + y = -1; 2x - 3y = -5
- b)x - 4y - 14 = 0; 5x - y - 13 = 0
- c)2x - y = 1 ; 3x + 2y = 0
- d)2x + 5y = -11; 4x + 10y = -23
Correct answer is option 'B'. Can you explain this answer?
A pair of linear equations which has a unique solution x = 2, y = - 3 is
a)
x + y = -1; 2x - 3y = -5
b)
x - 4y - 14 = 0; 5x - y - 13 = 0
c)
2x - y = 1 ; 3x + 2y = 0
d)
2x + 5y = -11; 4x + 10y = -23
|
Vikram Kapoor answered |
x - 4y -14 = 0
x = 4y+14
putting this in 5x - y -13 = 0
5(4y+14) - y -13 =0
19y = -57
y = -3
putting y = -3 in x = 4y+14
x = 4(-3)+14
x = 2
so option b is correct
If am ≠ bl, then the system of equations, ax + by = c, lx + my = n- a)has a unique solution
- b)has no solution
- c)has infinitely many solutions
- d)may or may not have a solution
Correct answer is option 'A'. Can you explain this answer?
If am ≠ bl, then the system of equations, ax + by = c, lx + my = n
a)
has a unique solution
b)
has no solution
c)
has infinitely many solutions
d)
may or may not have a solution
|
|
Vivek Rana answered |
If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.
Given,
Pair of lines represented by the equations
ax + by = c
lx + my = n
For unique solution
For infinite solutions
For no solution
Given,
This can be transformed into
Therefore, If am ≠ bl, then the equations ax+by=c, lx+my=n has a unique solution.
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digit of number get reversed. The number is- a)25
- b)72
- c)63
- d)36
Correct answer is option 'D'. Can you explain this answer?
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digit of number get reversed. The number is
a)
25
b)
72
c)
63
d)
36
|
Avinash Patel answered |
Lets,
First digit number = x
Second digit number = y
Number = (x+10y)
A/Q,
x + y = 9 ...................... (i)
A/Q,
(x+10y) = (10x+y) + 27
x + 10y = 10x + y +27
9x - 9y = 27
9(x - y) = 27
x - y = 27/9
x - y = 3 ......................... (ii)
Equation (i) and (ii) we get,
x = 3
Putting the value of x in eq.(i)
we get,
y = 6
Number = (10x +y)
= 10 x 3 + 6
= 30 + 6
= 36
The sum of ages of A and B is 50 years. A said to B, “I am twice as old as you were when I was as old as you are. Find the present age of B.- a)28
- b)20
- c)24
- d)12
Correct answer is option 'B'. Can you explain this answer?
The sum of ages of A and B is 50 years. A said to B, “I am twice as old as you were when I was as old as you are. Find the present age of B.
a)
28
b)
20
c)
24
d)
12
|
|
Vivek Rana answered |
Let the ages of A and B be a and b
Going by the statement step by step
A says “I am twice as old”=A says that age is twice some number which is a=2( _ )
"as you were" which talks about past, means B’s age some times ago...which is b-(how many years ago)
So, a=2(b- (how many years ago))
“when I was as old as you are" = when A was B’s age now= When A was b years old. So no. of years from now to back then will be A’s age now minus A’s age then =a-b
a=2(b-(a-b))
a=4b-2a
a=4b/3 …..1
Also a+b=49
a=49-b …..2
From 1 and 2
49-b=4b/3
4b/3+b=49
7b/3=49
b=49*3/7=21 years
a=28 years
Going by the statement step by step
A says “I am twice as old”=A says that age is twice some number which is a=2( _ )
"as you were" which talks about past, means B’s age some times ago...which is b-(how many years ago)
So, a=2(b- (how many years ago))
“when I was as old as you are" = when A was B’s age now= When A was b years old. So no. of years from now to back then will be A’s age now minus A’s age then =a-b
a=2(b-(a-b))
a=4b-2a
a=4b/3 …..1
Also a+b=49
a=49-b …..2
From 1 and 2
49-b=4b/3
4b/3+b=49
7b/3=49
b=49*3/7=21 years
a=28 years
The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:- a)One solution
- b)Infinitely many solutions
- c)No solutions
- d)Two solutions
Correct answer is option 'C'. Can you explain this answer?
The pair of linear equations x + y + 10 = 0 and x + y – 7 = 0 has:
a)
One solution
b)
Infinitely many solutions
c)
No solutions
d)
Two solutions
|
Gaurav Kumar answered |
We have a1, a2 the coefficients of x2,b1 and b2 coefficients of x and c1 and c2 the constant terms.
So,
a1a2=b1b2c1c2which is a case of parallel lines which which never meet. So there are no solutions obtainable for these equations.
So,a1a2=b1b2c1c2which is a case of parallel lines which which never meet. So there are no solutions obtainable for these equations.Find the solution to the following system of linear equations:
x-2y = 6
2x+y = 17- a)(8,1)
- b)(12,3)
- c)(1,2)
- d)(10,2)
Correct answer is option 'A'. Can you explain this answer?
Find the solution to the following system of linear equations:
x-2y = 6
2x+y = 17
x-2y = 6
2x+y = 17
a)
(8,1)
b)
(12,3)
c)
(1,2)
d)
(10,2)
|
Thor Kss answered |
X-2y=6 and 2x+y=17
by eliminating
x-2y=6*2
2x+y=17*1
2x will be cancelled
then y will be 1
and when we value of y in equation 1
we get x=8
by eliminating
x-2y=6*2
2x+y=17*1
2x will be cancelled
then y will be 1
and when we value of y in equation 1
we get x=8
The pair of equations x = 2 and y = – 3 has- a)no solution
- b)two solutions
- c)infinitely many solutions
- d)one solution
Correct answer is option 'D'. Can you explain this answer?
The pair of equations x = 2 and y = – 3 has
a)
no solution
b)
two solutions
c)
infinitely many solutions
d)
one solution
|
Ishan Choudhury answered |
Here a unique solution of each variable of a pair of linear equations is given, therefore, it has one solution of a system of linear quations.
The sum of two numbers is 45 and one is twice the other. What is the smaller number?
- a)30
- b)35
- c)15
- d)25
Correct answer is option 'C'. Can you explain this answer?
The sum of two numbers is 45 and one is twice the other. What is the smaller number?
a)
30
b)
35
c)
15
d)
25
|
Kailash mukherjee answered |
To solve this problem, we can use algebraic equations. Let's assume that the smaller number is x.
Given that one number is twice the other, we can express the larger number in terms of the smaller number as:
Larger number = 2x
And the sum of the two numbers is 45, so we can write the equation:
x + 2x = 45
Simplifying the equation, we have:
3x = 45
Dividing both sides of the equation by 3, we get:
x = 15
Therefore, the smaller number is 15.
So, option C, 15, is the correct answer.
Given that one number is twice the other, we can express the larger number in terms of the smaller number as:
Larger number = 2x
And the sum of the two numbers is 45, so we can write the equation:
x + 2x = 45
Simplifying the equation, we have:
3x = 45
Dividing both sides of the equation by 3, we get:
x = 15
Therefore, the smaller number is 15.
So, option C, 15, is the correct answer.
The pair of equations y = 0 and y = - 7 has- a)one solution
- b)two solutions
- c)infinitely many solutions
- d)no solution
Correct answer is option 'D'. Can you explain this answer?
The pair of equations y = 0 and y = - 7 has
a)
one solution
b)
two solutions
c)
infinitely many solutions
d)
no solution
|
|
Gaurav Kumar answered |
The equation are y=0 and y=-7
y=0 is on the x-axis and y=-7 is the line parallel to the x-axes at a distance 7 units from y=0
The line will be parallel
if we try to solve these equations we get 0=7 which is absurd.
So the equations are inconsistent.
Therefore there is no solution.
y=0 is on the x-axis and y=-7 is the line parallel to the x-axes at a distance 7 units from y=0
The line will be parallel
if we try to solve these equations we get 0=7 which is absurd.
So the equations are inconsistent.
Therefore there is no solution.
The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many solutions if –- a)k = 2
- b)k = 6
- c)k = 6
- d)k = 3
Correct answer is option 'A'. Can you explain this answer?
The pair of equations 3x + 4y = k, 9x + 12y = 6 has infinitely many solutions if –
a)
k = 2
b)
k = 6
c)
k = 6
d)
k = 3
|
Naina Sharma answered |
An equation has infinitely many solutions when the lines are coincident.
The lines are coincident when
So 3x + 4y = k, 9x + 12y = 6 are coincident when
The lines are coincident when
So 3x + 4y = k, 9x + 12y = 6 are coincident when
Find the solution to the following system of linear equations: 0.2x + 0.3y = 1.2
0.1x – 0.1y = 0.1- a)(1,2)
- b)(2,3)
- c)(3,2)
- d)(2,1)
Correct answer is option 'C'. Can you explain this answer?
Find the solution to the following system of linear equations: 0.2x + 0.3y = 1.2
0.1x – 0.1y = 0.1
0.1x – 0.1y = 0.1
a)
(1,2)
b)
(2,3)
c)
(3,2)
d)
(2,1)
|
|
Arun Sharma answered |
0.2x + 0.3y = 1.2
2x+3y=12 …..(1)
0.1x – 0.1y = 0.1x-y=1 ….(2)
From (2), x=1+y
Substituting the values of x in (1)
2(1+y)+3y=12
2+2y+3y=12
5y=10
y=2
x=1+2= 3
2x+3y=12 …..(1)
0.1x – 0.1y = 0.1x-y=1 ….(2)
From (2), x=1+y
Substituting the values of x in (1)
2(1+y)+3y=12
2+2y+3y=12
5y=10
y=2
x=1+2= 3
The pair of equations y = 0 and y = -7 has- a)one solution
- b)two solutions
- c)infinitely many solutions
- d)no solution
Correct answer is option 'D'. Can you explain this answer?
The pair of equations y = 0 and y = -7 has
a)
one solution
b)
two solutions
c)
infinitely many solutions
d)
no solution
|
|
Sunaina Singh answered |
The equation has parallel line have no solution.
Which of the following is not a solution of pair of equations 3x – 2y = 4 and 6x – 4y = 8?- a)x = 5, y = 3
- b)x = 2, y = 1
- c)x = 6, y = 7
- d)x = 4, y = 4
Correct answer is option 'A'. Can you explain this answer?
Which of the following is not a solution of pair of equations 3x – 2y = 4 and 6x – 4y = 8?
a)
x = 5, y = 3
b)
x = 2, y = 1
c)
x = 6, y = 7
d)
x = 4, y = 4
|
|
Vikram Kapoor answered |
3x – 2y = 4 and 6x – 4y = 8
Putting x=5 and y=3
LHS=3(5)-2(3)
15-6=9
RHS=4
LHS ≠ RHS
Also,
6(5)-4(3)=30-12=18 ≠ 8
Putting x=5 and y=3
LHS=3(5)-2(3)
15-6=9
RHS=4
LHS ≠ RHS
Also,
6(5)-4(3)=30-12=18 ≠ 8
Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is –- a)28 years
- b)30 years
- c)32 years
- d)34 years
Correct answer is option 'B'. Can you explain this answer?
Six years hence a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is –
a)
28 years
b)
30 years
c)
32 years
d)
34 years
|
Dr Manju Sen answered |
Let the present age of man is x and of son is y.
Six years hence,
Man’s age =x+6
Son’s age=y+6
Man’s age is 3 times son’s age
x+6=3(y+6)
x+6=3y+18
x=3y+12 …...1
Three years ago,
Man’s age =x-3
Son’s age=y-3
Man’s age was 9 times as of son
x-3=9(y-3)
x-3=9y-27
x=9y-24 ….2
From 1 and 2
3y+12=9y-24
6y=36
y=6
x=3*6+12=18+12=30 years
Six years hence,
Man’s age =x+6
Son’s age=y+6
Man’s age is 3 times son’s age
x+6=3(y+6)
x+6=3y+18
x=3y+12 …...1
Three years ago,
Man’s age =x-3
Son’s age=y-3
Man’s age was 9 times as of son
x-3=9(y-3)
x-3=9y-27
x=9y-24 ….2
From 1 and 2
3y+12=9y-24
6y=36
y=6
x=3*6+12=18+12=30 years
Which of the following points lie on the line 3x+2y=5 ?- a)(1, 1)
- b)(0, 1)
- c)(1, 0)
- d)(2, 1)
Correct answer is option 'A'. Can you explain this answer?
Which of the following points lie on the line 3x+2y=5 ?
a)
(1, 1)
b)
(0, 1)
c)
(1, 0)
d)
(2, 1)
|
Krishna Iyer answered |
When we are given only one equation and two variables we assume values for one variable and find the values for the other variable.
3x+2y=5
Let x=1
3*1+2y=5
2y=2
y=1 hence (1,1) lies on the line.
3x+2y=5
Let x=1
3*1+2y=5
2y=2
y=1 hence (1,1) lies on the line.
One equation of a pair of dependent linear equations is -5x + 7y = 2, the second equation can be :- a)-10x + 14y + 4 = 0
- b)-10x – 14x + 4 =
- c)10x – 14y = -4
- d)10x + 14y + 4 =0
Correct answer is option 'C'. Can you explain this answer?
One equation of a pair of dependent linear equations is -5x + 7y = 2, the second equation can be :
a)
-10x + 14y + 4 = 0
b)
-10x – 14x + 4 =
c)
10x – 14y = -4
d)
10x + 14y + 4 =0
|
|
Vikram Kapoor answered |
If a system of two linear equation is consistent system and has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.So we have 
which is satisfied by 10x – 14y = -4 only.
which is satisfied by 10x – 14y = -4 only.Can you explain the answer of this question below: How many solutions of the equation 15x – 14y + 11 = 0 are possible?
- A:
2
- B:
No solution
- C:
1
- D:
Infinite
The answer is d.
How many solutions of the equation 15x – 14y + 11 = 0 are possible?
2
No solution
1
Infinite
|
Rohit Sharma answered |
Since it is a linear equation, and the graph doesn’t end so it gives us infinite solutions, putting different values of x will give different values of y. For example , x = 0 ,y = 11/14 or y = 0, x = -11/15
The sum of the digits of a two digit number is 12. The number obtained by reversing its digits exceeds the given number by 18. Then the number is_____- a)75
- b)25
- c)52
- d)57
Correct answer is option 'D'. Can you explain this answer?
The sum of the digits of a two digit number is 12. The number obtained by reversing its digits exceeds the given number by 18. Then the number is_____
a)
75
b)
25
c)
52
d)
57
|
|
Neha Patel answered |
Let us assume x and y are the two digits of the number
Therefore, two-digit number is = 10x + y and the reversed number = 10y + x
Given:
x + y = 12
y = 12 – x (1)
Also given:
10y + x - 10x – y = 18
9y – 9x = 18
y – x = 2 (2)
Substitute the value of y from eqn 1 in eqn 2
12 – x – x = 2
12 – 2x = 2
2x = 10
x = 5
Therefore, y = 12 – x = 12 – 5 = 7
Therefore, the two-digit number is 10x + y = (10*5) + 7 = 57
Find the solution to the following system of linear equations:
2p+3q = 9
p – q = 2
- a)(4,2)
- b)(3,1)
- c)(2,-3)
- d)(-4,1)
Correct answer is option 'B'. Can you explain this answer?
Find the solution to the following system of linear equations:
2p+3q = 9
p – q = 2
2p+3q = 9
p – q = 2
a)
(4,2)
b)
(3,1)
c)
(2,-3)
d)
(-4,1)
|
Clifford Academy answered |
Alright, we have a system of two linear equations with two variables, p and q. Let's write them down:
1) 2p + 3q = 9
2) p - q = 2
Our goal is to find the values of p and q that satisfy both equations. We can use either the substitution method or the elimination method to solve this system. I'll use the substitution method here.
First, we'll solve the second equation for one of the variables. Let's solve for p:
p = q + 2
Now, we'll substitute this expression for p into the first equation:
2(q + 2) + 3q = 9
Distribute the 2:
2q + 4 + 3q = 9
Combine like terms:
5q + 4 = 9
Now, solve for q:
5q = 9 - 4
5q = 5
q = 1
Now that we have the value for q, we can plug it back into the expression for p:
p = q + 2
p = 1 + 2
p = 3
1) 2p + 3q = 9
2) p - q = 2
Our goal is to find the values of p and q that satisfy both equations. We can use either the substitution method or the elimination method to solve this system. I'll use the substitution method here.
First, we'll solve the second equation for one of the variables. Let's solve for p:
p = q + 2
Now, we'll substitute this expression for p into the first equation:
2(q + 2) + 3q = 9
Distribute the 2:
2q + 4 + 3q = 9
Combine like terms:
5q + 4 = 9
Now, solve for q:
5q = 9 - 4
5q = 5
q = 1
Now that we have the value for q, we can plug it back into the expression for p:
p = q + 2
p = 1 + 2
p = 3
The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is- a)inconsistent
- b)Both
- c)consistent
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is
a)
inconsistent
b)
Both
c)
consistent
d)
none of these
|
|
Amit Sharma answered |
a1 / a2 = b1 / b2 = c1 / c2
2/4 = 3/6 = 5/10
1/2 = 1/2 = 1/2
So, a1 / a2 = b1 / b2 = c1 / c2
When these are equal then it is consistent.
Therefore option (C) is correct .
2/4 = 3/6 = 5/10
1/2 = 1/2 = 1/2
So, a1 / a2 = b1 / b2 = c1 / c2
When these are equal then it is consistent.
Therefore option (C) is correct .
If a pair of linear equations has infinitely many solutions, then the lines representing them will be
- a)Parallel
- b)Intersecting lines
- c)Always intersecting
- d)coincident lines
Correct answer is option 'D'. Can you explain this answer?
If a pair of linear equations has infinitely many solutions, then the lines representing them will be
a)
Parallel
b)
Intersecting lines
c)
Always intersecting
d)
coincident lines
|
|
Ananya Das answered |
If two lines i.e. a pair of linear equations, has infinitely many solutions it means lines are overlapping each other i.e. coincident lines.
The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son. The present ages (in years) of the son and the father are, respectively. - a)4 and 24
- b)5 and 30
- c)6 and 36
- d)3 and 24
Correct answer is option 'C'. Can you explain this answer?
The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son. The present ages (in years) of the son and the father are, respectively.
a)
4 and 24
b)
5 and 30
c)
6 and 36
d)
3 and 24
|
|
Ååryañ answered |
For what value of ‘K’ will the system of equations 3x + y = 1, (2K – 1)x + (K – 1)y = 2K + 1 have no solution- a)3
- b)1
- c)-2
- d)2
Correct answer is option 'D'. Can you explain this answer?
For what value of ‘K’ will the system of equations 3x + y = 1, (2K – 1)x + (K – 1)y = 2K + 1 have no solution
a)
3
b)
1
c)
-2
d)
2
|
|
Ayush Sen answered |
I'm sorry, but your question appears to be incomplete. Please provide more context or information so I can assist you better.
- a)cut the x – axis
- b)coincide
- c)do not intersect at any point
- d)intersect only at a point
Correct answer is 'D'. Can you explain this answer?
|
|
Nisha Choudhury answered |
To sketch the graph of pair of linear equations in two variables, we draw two lines representing the equations.
If both the lines intersect at a point, then there exists a unique solution to the pair of linear equations. In such a case, the pair of linear equations is said to be consistent.
Can you explain the answer of this question below:The area of the triangle formed by the lines 2x + y = 6, 2x – y + 2 = 0 and the x – axis is
- A:
15sq. units
- B:
8sq. units
- C:
10sq. units
- D:
12sq. units
The answer is b.
The area of the triangle formed by the lines 2x + y = 6, 2x – y + 2 = 0 and the x – axis is
15sq. units
8sq. units
10sq. units
12sq. units
|
|
Arun Sharma answered |
Here are the two solutions of each of the given equations. 2x+y = 6
2x+y=0
The area bounded by the given lines and x−axis has been shaded in the graph.
∴
2x+y=0
The area bounded by the given lines and x−axis has been shaded in the graph.
∴
One equation of a pair of dependent linear equations is - 5x +7y = 2. The second equation can be- a)10x + 14y + 4 = 0
- b)-10x - 14y + 4 = 0
- c)-10x + 14y + 4 = 0
- d)10x - 14y = - 4
Correct answer is option 'D'. Can you explain this answer?
One equation of a pair of dependent linear equations is - 5x +7y = 2. The second equation can be
a)
10x + 14y + 4 = 0
b)
-10x - 14y + 4 = 0
c)
-10x + 14y + 4 = 0
d)
10x - 14y = - 4
|
|
Harshit Agrawal answered |
The given equn is. -5x+7y= 2 .
If we multiply -2 on both sides,
we get -5x(-2)+7y(-2) = 2(-2)
10x -14y = -4
Hence, other eqn is 10x-14y = -4.
Thus , D is the correct option
If we multiply -2 on both sides,
we get -5x(-2)+7y(-2) = 2(-2)
10x -14y = -4
Hence, other eqn is 10x-14y = -4.
Thus , D is the correct option
The pair of linear equations 2kx + 5y = 7, 6x – 5y = 11 has a unique solution if –
- a)k ≠ -3
- b)k = 3
- c)k = 5
- d)k = -5
Correct answer is option 'A'. Can you explain this answer?
The pair of linear equations 2kx + 5y = 7, 6x – 5y = 11 has a unique solution if –
a)
k ≠ -3
b)
k = 3
c)
k = 5
d)
k = -5
|
|
Rohit Sharma answered |
Given :
2 k x + 5 y – 7 = 0 ...( i )
6 x – 5 y – 1 = 0 ... ( ii )
Pair of linear equations has a unique solution.
We know for unique solution.
6 x – 5 y – 1 = 0 ... ( ii )
Pair of linear equations has a unique solution.
We know for unique solution.
Comparing from ( i ) and ( ii ) we have
Put these values in formula.
Thus we get answer many values of k but leaving k ≠ -3.
One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can be- a)– 10x – 14y + 4 = 0
- b)10x – 14y = – 4
- c)10x + 14y + 4 = 0
- d)– 10x + 14y + 4 = 0
Correct answer is option 'B'. Can you explain this answer?
One equation of a pair of dependent linear equations is – 5x + 7y = 2, then the second equation can be
a)
– 10x – 14y + 4 = 0
b)
10x – 14y = – 4
c)
10x + 14y + 4 = 0
d)
– 10x + 14y + 4 = 0
|
Veena patil answered |
Understanding Dependent Linear Equations
Dependent linear equations are those that represent the same line in a Cartesian plane. This means that one equation can be derived from the other by multiplying or dividing by a constant.
Given Equation
The given equation is:
-5x + 7y = 2
To find a dependent equation, we can multiply the entire equation by a non-zero constant.
Finding the Second Equation
Let's multiply the given equation by -2:
-2 * (-5x + 7y) = -2 * 2
This simplifies to:
10x - 14y = -4
Options to Evaluate
Now, let's analyze the options provided:
- Option A: -10x - 14y + 4 = 0
This rearranges to -10x - 14y = -4, which is not a dependent equation.
- Option B: 10x - 14y = -4
This is precisely what we derived from multiplying the original equation, confirming it is dependent.
- Option C: 10x + 14y + 4 = 0
This simplifies to 10x + 14y = -4, which is not equivalent.
- Option D: -10x + 14y + 4 = 0
This rearranges to -10x + 14y = -4, which is also not dependent.
Conclusion
Thus, the correct answer is:
- Option B: 10x - 14y = -4
This equation is a multiple of the original one, making it dependent and confirming that they represent the same line.
Dependent linear equations are those that represent the same line in a Cartesian plane. This means that one equation can be derived from the other by multiplying or dividing by a constant.
Given Equation
The given equation is:
-5x + 7y = 2
To find a dependent equation, we can multiply the entire equation by a non-zero constant.
Finding the Second Equation
Let's multiply the given equation by -2:
-2 * (-5x + 7y) = -2 * 2
This simplifies to:
10x - 14y = -4
Options to Evaluate
Now, let's analyze the options provided:
- Option A: -10x - 14y + 4 = 0
This rearranges to -10x - 14y = -4, which is not a dependent equation.
- Option B: 10x - 14y = -4
This is precisely what we derived from multiplying the original equation, confirming it is dependent.
- Option C: 10x + 14y + 4 = 0
This simplifies to 10x + 14y = -4, which is not equivalent.
- Option D: -10x + 14y + 4 = 0
This rearranges to -10x + 14y = -4, which is also not dependent.
Conclusion
Thus, the correct answer is:
- Option B: 10x - 14y = -4
This equation is a multiple of the original one, making it dependent and confirming that they represent the same line.
The pair of linear equations 2x + 5y = k, kx + 15y = 18 has infinitely many solutions if –- a)k = 3
- b)k = 6
- c)k = 9
- d)k = 18
Correct answer is option 'B'. Can you explain this answer?
The pair of linear equations 2x + 5y = k, kx + 15y = 18 has infinitely many solutions if –
a)
k = 3
b)
k = 6
c)
k = 9
d)
k = 18
|
|
Vivek Rana answered |
An equation has infinitely many solutions when the lines are coincident.
The lines are coincident when
So 2x + 5y = k, kx + 15y = 18 are coincident when
The lines are coincident when
So 2x + 5y = k, kx + 15y = 18 are coincident when
The value of x in mx + ny = c; nx – ny = c + 1 is
- a)x = (m + n) / (c + 1)
- b)x = (2c + 1) / (m + n)
- c)x = m + n
- d)x = 2c + 1
Correct answer is option 'B'. Can you explain this answer?
The value of x in mx + ny = c; nx – ny = c + 1 is
a)
x = (m + n) / (c + 1)
b)
x = (2c + 1) / (m + n)
c)
x = m + n
d)
x = 2c + 1
|
|
Mansi desai answered |
To find the value of x in the equation mx + ny = c, we need more information or another equation. The equation nx = 0 does not provide enough information to solve for x.
For what value of ‘K’ will the system of equations: 3x + y = 1, (2K – 1) x + (K – 1) y = 2K + 1 have no solution- a)3
- b)2
- c)1
- d)-2
Correct answer is option 'B'. Can you explain this answer?
For what value of ‘K’ will the system of equations: 3x + y = 1, (2K – 1) x + (K – 1) y = 2K + 1 have no solution
a)
3
b)
2
c)
1
d)
-2
|
|
Krishna Iyer answered |
is a case of parallel lines which never meet. So there are no solutions obtainable for these equations. So equations are inconsistent3x + y = 1, (2K – 1) x + (K – 1) y = 2K + 1
b1=1,b2=k-1,c1=-1,c2=-2k-1
Can you explain the answer of this question below:The pair of equations y = 0 and y = -7 has :
- A:
no solution
- B:
infinitely many solutions
- C:
one solution
- D:
two solutions
The answer is a.
The pair of equations y = 0 and y = -7 has :
no solution
infinitely many solutions
one solution
two solutions
|
|
Raghav Bansal answered |
y=0 is x-axis… since every point has y=0. y=-7 is a line parallel to x-axis passing through x=0,y=-7. So the two lines are parallel to each other and are inconsistent which means that it has no solutions because it will never meet.
Which of following is not a solution of 3a + b = 12 ?
- a)(3, 3)
- b)(5, -3)
- c)(4, 0)
- d)(2, 4)
Correct answer is option 'D'. Can you explain this answer?
Which of following is not a solution of 3a + b = 12 ?
a)
(3, 3)
b)
(5, -3)
c)
(4, 0)
d)
(2, 4)
|
Prashant Gujjar Pgv answered |
D correct h 3(2)+4=10this is not a solution
In elimination method _____________ is an important condition.- a)Equating either of the coefficients
- b)Equating only the y coefficient.
- c)Equating only the x co-efficient.
- d)Equating both the coefficients.
Correct answer is option 'A'. Can you explain this answer?
In elimination method _____________ is an important condition.
a)
Equating either of the coefficients
b)
Equating only the y coefficient.
c)
Equating only the x co-efficient.
d)
Equating both the coefficients.
|
|
Rajiv Gupta answered |
Elimination Method (by Equating Coefficients)
There is another method of eliminating a variable, than often used method i. e --------Suppose you are to solve
23x - 17y + 11=0 ------(1)
and 31x + 13y - 57 = 0 -------(2)
Now expressing x in terms of y would involve division by 23 or 31. Express y in terms of x, it would involve division by 17 or 13. You know that multiplication is more convenient than division, better to convert the division process into a multiplication process.
Multiplying the first equation by 13 viz., coefficient of y in (2), and second by 17 viz., coefficient of y in (1), you will get an equivalent system of equations. The new system has the advantage that y has the same numerical coefficient 17x13 in both the equations. When you add these new equations, the terms containing y would cancel out as these have opposite signs and the same numerical coefficient. Thus, y has been eliminated. Now proceed as before, and solve the system. This method of elimination is also called elimination by equating coefficients for obvious reasons.
Example: Solve the following system of equations using the elimination method by equating coefficients:
11x - 5y + 61 = 0 (1)
3x - 20y - 2 = 0 (2)
Solution: Let us multiply equation (1) by 3 and equation (2) by 11. This gives
33x - 15y + 183 = 0 (3)
and 33x - 220y - 22 = 0 (4)
Subtracting (4) from (3), you will get 205y + 205 = 0
, or y = - 1
Substituting this value of y in equation (2), you will get
3x - 20 * (- 1) - 2 = 0
or 3x = -18
or x = - 6
Thus, the required solution is
x = - 6 and y = -1.
Now you should verify; substitute x = - 6 and y = -1 in the given equations, you will notice both the equations are satisfied. Hence, the solution is correct
If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y are- a)½ and 1
- b)1 and 2
- c)2 and 1
- d)1 and ½
Correct answer is option 'B'. Can you explain this answer?
If 6x + 3y= 6xy ; 2x + 4y = 5xy, then the values of xand y are
a)
½ and 1
b)
1 and 2
c)
2 and 1
d)
1 and ½
|
Atharva Iyer answered |
The first equation is 6x + 3y = 6xy, which can be rewritten as 6x - 6xy = -3y.
Factoring out x from the left side gives: x(6 - 6y) = -3y.
Dividing both sides by (6 - 6y) gives: x = (-3y) / (6 - 6y).
The second equation is 2x + 4y = 5xy, which can be rewritten as 2x - 5xy = -4y.
Factoring out x from the left side gives: x(2 - 5y) = -4y.
Dividing both sides by (2 - 5y) gives: x = (-4y) / (2 - 5y).
Since both equations are equal to x, we can set the right sides equal to each other:
(-3y) / (6 - 6y) = (-4y) / (2 - 5y).
Cross multiplying gives: (-3y)(2 - 5y) = (-4y)(6 - 6y).
Expanding gives: -6y + 15y^2 = -24y + 24y^2.
Combining like terms gives: 15y^2 - 6y = 24y^2 - 24y.
Subtracting (15y^2 - 6y) from both sides gives: 0 = 9y^2 - 18y.
Factoring out y gives: 0 = y(9y - 18).
Setting each factor equal to zero gives: y = 0 or 9y - 18 = 0.
Solving the second equation for y gives: 9y = 18, y = 2.
Substituting y = 2 into the first equation gives: 6x + 3(2) = 6x(2), 6x + 6 = 12x.
Subtracting 6x from both sides gives: 6 = 6x.
Dividing both sides by 6 gives: x = 1.
Therefore, the values of x and y are x = 1 and y = 2.
Answer: a) x = 1 and y = 2.
Factoring out x from the left side gives: x(6 - 6y) = -3y.
Dividing both sides by (6 - 6y) gives: x = (-3y) / (6 - 6y).
The second equation is 2x + 4y = 5xy, which can be rewritten as 2x - 5xy = -4y.
Factoring out x from the left side gives: x(2 - 5y) = -4y.
Dividing both sides by (2 - 5y) gives: x = (-4y) / (2 - 5y).
Since both equations are equal to x, we can set the right sides equal to each other:
(-3y) / (6 - 6y) = (-4y) / (2 - 5y).
Cross multiplying gives: (-3y)(2 - 5y) = (-4y)(6 - 6y).
Expanding gives: -6y + 15y^2 = -24y + 24y^2.
Combining like terms gives: 15y^2 - 6y = 24y^2 - 24y.
Subtracting (15y^2 - 6y) from both sides gives: 0 = 9y^2 - 18y.
Factoring out y gives: 0 = y(9y - 18).
Setting each factor equal to zero gives: y = 0 or 9y - 18 = 0.
Solving the second equation for y gives: 9y = 18, y = 2.
Substituting y = 2 into the first equation gives: 6x + 3(2) = 6x(2), 6x + 6 = 12x.
Subtracting 6x from both sides gives: 6 = 6x.
Dividing both sides by 6 gives: x = 1.
Therefore, the values of x and y are x = 1 and y = 2.
Answer: a) x = 1 and y = 2.
A train overtakes two persons who are walking at the rate of 8 kmph and 12 kmph in the same direction in which the train is going, and passes them completely in 9 and 10 seconds respectively. What is the length of the train?- a)200 m
- b) 500 m
- c) 100 m
- d)300 m
Correct answer is option 'C'. Can you explain this answer?
A train overtakes two persons who are walking at the rate of 8 kmph and 12 kmph in the same direction in which the train is going, and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
a)
200 m
b)
500 m
c)
100 m
d)
300 m
|
|
Rajiv Gupta answered |
8 kmph = (8 x 5/18) = 20/9 m/sec
4 kmph = (12 x 5/18 = 10/3 m/sec
18 9
Let the length of the train be x metres and its speed by y m/sec.
Then, [x/(y - 20/9)] = 9 and [x/(y - 10/3)] = 10
Therefore 9y - 20 = x and 10y - 100/3 = x
=> 9y - 20 = 10y - 100/3
solving: y = 40/3
putting value of y in (1):
9 . (40/3) - 20 = x
so, x = 100 m
On solving, we get: x = 100.
Therefore Length of the train is 100 m.
The Index of Coincidence for English language is approximately- a)0.068
- b)0.038
- c)0.065
- d)0.048
Correct answer is option 'C'. Can you explain this answer?
The Index of Coincidence for English language is approximately
a)
0.068
b)
0.038
c)
0.065
d)
0.048
|
Hariteja Patnala answered |
Yes actually you said option C is correct it is actually correct but the actual answer is different
actual answer for index of coincide of English language is 0.0 667
index of coincide is a technique to find the probability of the repeating letters in an encrypted text
the index of coincide value is calculated on the basis of the probability of occurrence of a specified letter and the probability of comparing it to the same letter from the second text
so this is my answer for index of coincide of English language is 0.0667 but you have given that C is correct option
actual answer for index of coincide of English language is 0.0 667
index of coincide is a technique to find the probability of the repeating letters in an encrypted text
the index of coincide value is calculated on the basis of the probability of occurrence of a specified letter and the probability of comparing it to the same letter from the second text
so this is my answer for index of coincide of English language is 0.0667 but you have given that C is correct option
Can you explain the answer of this question below:The sum of the numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. The fraction is
- A:
7/11
- B:
-5/13
- C:
-7/11
- D:
5/13
The answer is d.
The sum of the numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. The fraction is
7/11
-5/13
-7/11
5/13
|
|
Rahul Kapoor answered |
Let the numer be x & denom be y..
x+y= 18....(1)
x/y+2 =1/3
3x=y+2
x=(y+2)/3
put this value in eq 1
x+y=18
(y+2)/3+y=18
(y+2+3y= 18x3
4y+2 =54
4y=54-2
4y= 52
y= 52/4
y= 13
put the value of y in eq 1
x+y=18
x+ 13=18
x= 18- 13
x= 5
Hence req. fraction = x/ y = 5/13
A lending library has a fixed charge for the first two days and an additional charge for each day thereafter. Sunil paid Rs 28 for a book kept for seven days, while Sohail paid Rs 32 for the book he kept for nine days. Find the charge for each extra day.- a)Rs 3
- b)Rs 20
- c)Rs 2
- d)Rs 18
Correct answer is option 'C'. Can you explain this answer?
A lending library has a fixed charge for the first two days and an additional charge for each day thereafter. Sunil paid Rs 28 for a book kept for seven days, while Sohail paid Rs 32 for the book he kept for nine days. Find the charge for each extra day.
a)
Rs 3
b)
Rs 20
c)
Rs 2
d)
Rs 18
|
|
Abhishek Bhai answered |
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