#### Solved Examples and Worksheet for Solving Systems of Equations using Elimination Method

Q1Solve the linear system.
3x + 4y = 32
5x - 4y = 0

A. (3, 5)
B. (3, 4)
C. (4, 5)
D. (5, 5)

Step: 1
3x + 4y = 32 ...........(1)
5x - 4y = 0 .............(2)
Step: 2
3x + 4y = 32
Step: 3
5x -  4y = 0
____________
Step: 4
8x       =  32
Step: 5
x = 4
[Solve for x.]
Step: 6
3(4) + 4y = 32
[Substitute x = 4 in equation 1.]
Step: 7
12 + 4y = 32
[Multiply.]
Step: 8
4y = 20
[Subtract 12 from each side.]
Step: 9
y = 5
[Solve for y.]
Step: 10
The solution for the linear system is (4, 5).
Correct Answer is :   (4, 5)
Q2Solve the linear system.
- x + y = - 20
17x - y = 68

A. (3, 17)
B. (3, - 17)
C. (17, 3)
D. (17, - 17)

Step: 1
- x + y = - 20 .........(1)
17x - y = 68 ..........(2)
Step: 2
- x + y = - 20
Step: 3
17x - y = 68
___________
Step: 4
16x       = 48
Step: 5
x = 3
[Solve for x.]
Step: 6
- 3 + y = - 20
[Substitute x = 3 in Equation 1.]
Step: 7
y = - 17
[Solve for y.]
Step: 8
So, the solution for the linear system is (3, - 17).
Correct Answer is :   (3, - 17)
Q3Solve:
4x - 5y = -8
6x + 5y = 38

A. (2, 5)
B. (3, 5)
C. (3, 4)
D. (4, 3)

Step: 1
4x - 5y = -8.............(1)
6x + 5y = 38..............(2)
Step: 2
4x - 5y = -8
Step: 3
6x + 5y = 38
______________
Step: 4
10x        = 30
Step: 5
x = 3
[Solve for x.]
Step: 6
4(3) - 5y = -8
[Replace x with 3 in Equation 1.]
Step: 7
y = 4
[Solve for y.]
Step: 8
The solution for the linear system is (3, 4).
Correct Answer is :   (3, 4)
Q4Solve the linear system.
- 3x - y = - 21
- 3x + y = -9

A. (5, 7)
B. (5, 6)
C. (4, 6)
D. (6, 6)

Step: 1
- 3x - y = - 21..........(1)
- 3x + y = -9..........(2)
Step: 2
- 3x - y = - 21
Step: 3
- 3x + y = -9
______________
Step: 4
- 6x        = -30
Step: 5
x = 5
[Solve for x.]
Step: 6
- 3(5) - y = - 21
[Substitute x = 5 in Equation 1.]
Step: 7
y = 6
[Solve for y.]
Step: 8
The solution for the linear system is (5, 6).
Correct Answer is :   (5, 6)
Q5Solve the linear system.
x - 3y = -2
- x + 6y = 11

A. (8, 2)
B. (7, 3)
C. (7, 6)
D. (7, 2)

Step: 1
x - 3y = -2...........(1)
- x + 6y = 11.............(2)
Step: 2
x - 3y = -2
[Equation 1.]
Step: 3
- x + 6y = 11
____________
[Equation 2.]
Step: 4
3y = 9
Step: 5
y = 3
[Solve for y.]
Step: 6
x - 3(3) = -2
[Substitute y = 3 in Equation 1.]
Step: 7
x = 7
[Solve for x.]
Step: 8
So, the solution for the linear system is (7, 3).
Correct Answer is :   (7, 3)
Q6Solve the linear system.
3x + y = 13
- 4x - 5y = 1

A. (6, - 5)
B. (13, 1)
C. (-14, 55)
D. (-5, 28)

Step: 1
3x + y = 13 .....(1)
- 4x - 5y = 1 .....(2)
Step: 2
Eliminate x from both the equations by making the coefficient of x in one equation opposite to the other.
Step: 3
12x + 4y = 52
[Multiply Equation 1 by 4.]
Step: 4
- 12x - 15y = 3
_______________
[Multiply Equation 2 by 3.]
Step: 5
-11y = 55
Step: 6
y = - 5
[Solve for y.]
Step: 7
3x + (- 5) = 13
[Substitute y = - 5 in Equation 1.]
Step: 8
x = 6
[Solve for x.]
Step: 9
The solution for the linear system is (6, - 5).
Correct Answer is :   (6, - 5)
Q7Solve the linear system.
x - 5y = -37
- 4x - 5y = -77

A. (8, 9)
B. (- 8, 9)
C. (- 8, 0)
D. (8, - 9)

Step: 1
x - 5y = -37
[Equation 1.]
Step: 2
- 4x - 5y = -77
[Equation 2.]
Step: 3
4x - 20y = -148
[Multiply Equation 1 by 4.]
Step: 4
 4x - 20y =  -148 - 4x - 5y = -77 - 25y = -225
Step: 5
y = 9
[Solve for y.]
Step: 6
x - 5(9) = -37
[Substitute y = 9 in Equation 1.]
Step: 7
x - 45 = -37
[Multiply.]
Step: 8
x = -37 + 45
Step: 9
x = 8
[Solve for x.]
Step: 10
So, the solution for the linear system is (8, 9).
Correct Answer is :   (8, 9)
Q8Which of the following solutions satisfies the linear system?
3x - y = - 1
- 2x + 3y = -11

A. (- 3, 2)
B. (-5, 2)
C. (- 3, -5)
D. (- 2, -5)

Step: 1
3x - y = - 1 .....(1)
- 2x + 3y = -11 .....(2)
Step: 2
9x - 3y = - 3
[Multiply Equation 1 by 3.]
Step: 3
- 2x + 3y = -11
______________

Step: 4
7x = -14
Step: 5
x = - 2
[Solve for x.]
Step: 6
3(- 2) - y = - 1
[Substitute x = - 2 in Equation 1.]
Step: 7
y = -5
[Solve for y.]
Step: 8
Solution for the linear system is (- 2, -5).
Correct Answer is :   (- 2, -5)
Q9Which of the following ordered pairs satisfies the linear system?
- 4x + 3y = - 15
3y = 3 + 2x

A. (8, 7)
B. (- 9, 8)
C. (-10, - 7)
D. (9, 7)

Step: 1
- 4x + 3y = - 15 .....(1)
3y = 3 + 2x .....(2)
Step: 2
- 4x + 3y = - 15
[Equation 1.]
Step: 3
2x - 3y = - 3
____________
[Rearrange Equation 2.]
Step: 4
-2x        = - 18
Step: 5
x = 9
[Solve for x.]
Step: 6
- 4(9) + 3y = - 15
[Replace x with 9 in Equation 1.]
Step: 7
- 36 + 3y = - 15
[Multiply.]
Step: 8
3y = 21
Step: 9
y = 7
[Solve for y.]
Step: 10
Solution for the linear system is (9, 7).
Correct Answer is :   (9, 7)
Q10Which of the following ordered pairs satisfies the linear system?
9x + 7y = -15
9x - 7y = -57

A. (4, - 3)
B. (4, 3)
C. (- 4, 3)
D. (- 4, - 3)

Step: 1
9x + 7y = -15
[Equation 1.]
Step: 2
9x - 7y = -57
[Equation 2.]
Step: 3
18x     = -72
Step: 4
x = - 4
[Solve for x.]
Step: 5
9(- 4) + 7y = -15
[Replace x with - 4 in Equation 1.]
Step: 6
y = 3
[Solve for y.]
Step: 7
The solution for the linear system is (- 4, 3).
Correct Answer is :   (- 4, 3)
Q11Which of the following ordered pairs satisfies the linear system?
- x + y = - 2
3x - y = - 4

A. (-5, - 3)
B. (3, -5)
C. (- 3, -5)
D. (-5, 3)

Step: 1
- x + y = - 2
[Equation 1.]
Step: 2
3x - y = - 4
____________
[Equation 2.]
Step: 3
2x       = - 6
[Add Equation 1 and Equation 2.]
Step: 4
x = - 3
[Solve for x.]
Step: 5
- (- 3) + y = - 2
[Replace x with - 3 in Equation 1.]
Step: 6
y = -5
[Solve for y.]
Step: 7
The solution for the linear system is (- 3, -5).
Correct Answer is :   (- 3, -5)
Q12Solve the linear system.
5x + 4y = -1
- 4x + 5y = 9

A. (0, 1)
B. (-1, 1)
C. (0, 2)
D. (1, -1)

Step: 1
5x + 4y = -1 .....(1)
- 4x + 5y = 9 .....(2)
Step: 2
20x + 16y = -4
[Multiply Equation 1 by 4.]
Step: 3
- 20x + 25y = 45
________________
[Multiply Equation 2 by 5.]
Step: 4
41y = 41
Step: 5
y = 1
[Solve for y.]
Step: 6
5x + 4(1) = -1
[Substitute y = 1 in Equation 1.]
Step: 7
5x + 4 = -1
[Multiply.]
Step: 8
5x = -5
[Subtract 4 from each side.]
Step: 9
x = -1
[Solve for x.]
Step: 10
The solution for the linear system is (-1, 1).
Correct Answer is :   (-1, 1)
Q13Solve the linear system.
x + 3y = -5
- 2x + 3y = -17

A. (- 4 , - 3)
B. (4 , - 3)
C. (- 4 , 3)
D. (4 , 3)

Step: 1
x + 3y = -5 .....(1)
- 2x + 3y = -17 .....(2)
Step: 2
2x + 6y = -10
[Multiply Equation 1 by 2.]
Step: 3
- 2x + 3y = -17
_____________
[Multiply Equation 2 by 1.]
Step: 4
9y = -27
Step: 5
y = - 3
[Solve for y.]
Step: 6
x + 3(- 3) = -5
[Replace y with - 3 in Equation 1.]
Step: 7
x - 9 = -5
[Multiply.]
Step: 8
x = 4
Step: 9
The solution for the linear system is (4, - 3).
Correct Answer is :   (4 , - 3)
Q14Solve the linear system.
x - 4y = 8
- 4x + 4y = 4

A. (4 , 3)
B. (4 , - 3)
C. (- 4 , 3)
D. (- 4 , - 3)

Step: 1
4x - 16y = 32
[Multiply equation 1 by 4.]
Step: 2
- 4x + 4y = 4
_______________
[Multiply equation 2 by 1.]
Step: 3
-12y = 36
Step: 4
y = - 3
[Solve for y.]
Step: 5
x - 4(- 3) = 8
[Substitute y = - 3 in Equation 1.]
Step: 6
x + 12 = 8
[Multiply.]
Step: 7
x = 8 - 12
[Subtract 12 from each side.]
Step: 8
x = - 4
[Solve for x.]
Step: 9
The solution for the linear system is (- 4, - 3)
Correct Answer is :   (- 4 , - 3)
Q15Solve the linear system.
x - 2y = - 4
- 5x + 2y = 20

A. (4 , 0)
B. (0, - 4 )
C. (0, 4 )
D. (- 4 , 0)

Step: 1
5x - 10y = - 20
[Multiply Equation 1 by 5.]
Step: 2
- 5x + 2y = 20
_______________
[Multiply Equation 2 by 1.]
Step: 3
-8y = 0
Step: 4
y = 0
[Solve for y.]
Step: 5
x - 2(0) = - 4
[Replace y with 0 in Equation 1.]
Step: 6
x - 0 = - 4
[Multiply.]
Step: 7
x = - 4
[Solve for x.]
Step: 8
The solution for the linear system is (- 4, 0).
Correct Answer is :   (- 4 , 0)