Solving Systems of Equations using Elimination Method-Algebra1-Solved Examples

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)

Solutions

Step: 1

3x + 4y = 32 ...........(1)
5x - 4y = 0 .............(2)

Step: 2

3x + 4y = 32

Step: 3

5x - 4y = 0
____________

Step: 4

8x = 32

[Add the equations.]

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)

Solutions

Step: 1

- x + y = - 20 .........(1)
17x - y = 68 ..........(2)

Step: 2

- x + y = - 20

Step: 3

17x - y = 68
___________

Step: 4

16x = 48

[Add the equations.]

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)

Solutions

Step: 1

4x - 5y = -8.............(1)
6x + 5y = 38..............(2)

Step: 2

4x - 5y = -8

Step: 3

6x + 5y = 38
______________

Step: 4

10x = 30

[Add the equations.]

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)

Solutions

Step: 1

- 3x - y = - 21..........(1)
- 3x + y = -9..........(2)

Step: 2

- 3x - y = - 21

Step: 3

- 3x + y = -9
______________

Step: 4

- 6x = -30

[Add the equations.]

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)

Solutions

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

[Add the equations.]

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)

Solutions

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

[Add the equations.]

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)

Solutions

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

[Add the Equations.]

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

[Add 45 to both sides.]

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)

Solutions

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

[Add the equations.]

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)

Solutions

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

[Add the equations.]

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

[Add 36 on each side.]

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)

Solutions

Step: 1

9x + 7y = -15

[Equation 1.]

Step: 2

9x - 7y = -57

[Equation 2.]

Step: 3

18x = -72

[Add Equations 1 and 2.]

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)

Solutions

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)

Solutions

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

[Add the equations.]

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)

Solutions

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

[Add the equations.]

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

[Add 9 to both sides.]

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)

Solutions

Step: 1

4x - 16y = 32

[Multiply equation 1 by 4.]

Step: 2

- 4x + 4y = 4
_______________

[Multiply equation 2 by 1.]

Step: 3

-12y = 36

[Add the equations.]

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)

Solutions

Step: 1

5x - 10y = - 20

[Multiply Equation 1 by 5.]

Step: 2

- 5x + 2y = 20
_______________

[Multiply Equation 2 by 1.]

Step: 3

-8y = 0

[Add the equations.]

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)

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

Related Worksheet

Related Topic

HighSchool Math