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

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

Q1Which of the following ordered pairs satisfies the linear system?
x - y = 6
4x + 9y = -28

A. (2, - 4)
B. (2, 4)
C. (- 2, 4)
D. (- 2, - 4)

Solutions

Step: 1

y = x - 6

[Rearrange Equation 1.]

Step: 2

4x + 9(x - 6) = -28

[Substitute y = (x - 6) in equation 2.]

Step: 3

13x - 54 = -28

[Combine like terms.]

Step: 4

13x = 26

[Add 54 to both sides.]

Step: 5

x = 2

[Divide each side by 13.]

Step: 6

y = x - 6 = 2 - 6

[Substitute x = 2 in the revised equation 1.]

Step: 7

y = -4

[Simplify.]

Step: 8

The solution for the linear system is (2, -4).

Correct Answer is : (2, - 4)

Q2Which of the following ordered pairs satisfies the linear system?
2x - y = 0
x - 4y = 0

A. (0, 0)
B. (2, - 4)
C. (- 2, 4)
D. (2, 4)

Solutions

Step: 1

y = 2x

[Rearrange Equation 1.]

Step: 2

x - 4(2x) = 0

[Substitute y = 2x in Equation 2.]

Step: 3

- 7x = 0

[Combine like terms.]

Step: 4

x = 0

[Divide each side by - 7.]

Step: 5

y = 2x = 2(0)

[Substitute x = 0 in revised Equation 1.]

Step: 6

y = 0

[Simplify.]

Step: 7

The solution for the linear system is (0, 0).

Correct Answer is : (0, 0)

Q3Which of the following ordered pairs satisfies the linear system?
5x - 3y = -3
- x + 3y = -21
A. (- 6, - 9)
B. (6, 6)
C. (-28, -52)
D. (6, 5)

Solutions

Step: 1

- x + 3y = -21

[Original equation 2.]

Step: 2

x = 21 + 3y

[Revise equation 2.]

Step: 3

5(21 + 3y) - 3y = -3

[Replace x with 21 + 3y in Equation 1.]

Step: 4

12y + 105 = -3

[Combine like terms.]

Step: 5

12y = -108

[Subtract 105 from each side.]

Step: 6

y = - 9

[Divide each side by 12.]

Step: 7

x = 21 + 3y = 21 + 3(- 9)

[Replace y with - 9 in the revised Equation 2.]

Step: 8

x = - 6

[Simplify.]

Step: 9

The solution for the linear system is (- 6, - 9).

Correct Answer is : (- 6, - 9)

Q4Which of the following ordered pairs satisfies the linear system?
- x + y = 8
6x - 5y = -31
A. (9, 17)
B. (- 9, 17)
C. (9, - 17)
D. (- 9, - 17)

Solutions

Step: 1

y = x + 8

[Rearrange Equation 1.]

Step: 2

6x - 5(x + 8) = -31

[Replace y with x + 8 in Equation 2.]

Step: 3

x - 40 = -31

[Combine like terms.]

Step: 4

x = 9

[Add 40 to both sides.]

Step: 5

y = 9 + 8

[Substitute x = 9 in the revised Equation 1.]

Step: 6

y = 17

[Simplify.]

Step: 7

The solution for the linear system is (9, 17).

Correct Answer is : (9, 17)

Q5Find the solution of the system of linear equations.
5x + 3y = 21
x - 3y = 3

A. (4, 13)
B. (4, - 13)
C. (- 4, - 13)
D. (- 4, 13)

Solutions

Step: 1

5x + 3y = 21

[Equation 1.]

Step: 2

x - 3y = 3

[Equation 2.]

Step: 3

x = 3y + 3

[Revised Equation 2.]

Step: 4

5(3y + 3) + 3y = 21

[Substitute x = 3y + 3 in Equation 1.]

Step: 5

18y + 15 = 21

[Combine like terms.]

Step: 6

18y = 6

[Subtract 15 from each side.]

Step: 7

y = 13

[Divide each side by 18.]

Step: 8

x = 3y + 3 = 3(13) + 3

[Replace y with 13 in the revised Equation 2.]

Step: 9

x = 4

[Simplify.]

Step: 10

The solution for the linear system is (4, 13).

Correct Answer is : (4, 13)

Q6Which of the following ordered pairs satisfies the linear system?
4x + 3y = 17
- x + 3y = 7
A. (- 2, 3)
B. (- 2, - 3)
C. (2, - 3)
D. (2, 3)

Solutions

Step: 1

4x + 3y = 17 .....(1)
- x + 3y = 7 .....(2)

Step: 2

Equation 2 can be rearranged as x = 3y - 7 so that x in equation 1 can be replaced with this in order to solve the linear system.

Step: 3

4(3y - 7) + 3y = 17

[Replace x with 3y - 7 in Equation 1.]

Step: 4

15y - 28 = 17

[Combine like terms.]

Step: 5

15y = 45

[Add 28 to both sides.]

Step: 6

y = 3

[Divide each side by 15.]

Step: 7

x = 3y - 7 = 3(3) - 7

[Replace y with 3 in the revised Equation 2.]

Step: 8

x = 2

[Simplify.]

Step: 9

The solution for the linear system is (2, 3).

Correct Answer is : (2, 3)

Q7Which of the following ordered pairs satisfies the linear system?
- 16x + 3y = -97
x - y = 2
A. (7, 5)
B. (- 7, - 5)
C. (7, - 5)
D. (- 7, 5)

Solutions

Step: 1

- 16x + 3y = -97 - - - - - - - - (1)

Step: 2

x - y = 2 - - - - - - - - (2)

Step: 3

x = y + 2

[Rearrange Equation 2.]

Step: 4

- 16(y + 2) + 3y = -97

[Substitute y + 2 for x in Equation 1.]

Step: 5

- 13y - 32 = -97

[Combine like terms.]

Step: 6

- 13y = -65

[Add 32 to both sides.]

Step: 7

y = 5

[Divide each side by - 13.]

Step: 8

x = y + 2 = 5 + 2

[Replace y with 5 in the revised Equation 2.]

Step: 9

x = 7

[Simplify.]

Step: 10

So, the solution for the linear system is (7, 5).

Correct Answer is : (7, 5)

Q8Solve the system by substitution:
6x - 3y = 15
- 4x + 2y = - 10
A. No solution
B. (3, 0)
C. Infinite solutions
D. (2, 5)

Solutions

Step: 1

6x - 3y = 15

[First equation.]

Step: 2

- 3y = 15 - 6x

[Subtract 6x from the two sides of the equation.]

Step: 3

y = - 5 + 2x

[Divide through out by - 3 from each side.]

Step: 4

- 4x + 2y = - 10

[Second equation.]

Step: 5

- 4x + 2(- 5 + 2x) = - 10

[Substitute the values.]

Step: 6

- 4x - 10 + 4x = - 10

Step: 7

- 10 = - 10

Step: 8

The above equation is always true, the number of solutions is infinite.

Correct Answer is : Infinite solutions

Q9Solve the system by substitution:
2x + 12y = 10
6x = - 36y + 36

A. (36, 0)
B. (6, 6)
C. Infinite solution
D. No solution

Solutions

Step: 1

6x = - 36y + 36

[Second equation.]

Step: 2

x = - 6y + 6

[Divide throughout by 6 .]

Step: 3

2x + 12y = 10

[First equation.]

Step: 4

2(- 6y + 6) + 12y = 10

[Substitute the values.]

Step: 5

- 12y + 12 + 12y = 10

Step: 6

12 = 10

[Contradiction.]

Step: 7

So, there is no solution, the system is inconsistent.

Correct Answer is : No solution

Q10Which of the following ordered pairs satisfies the linear system?
x - y = 6 [Equation 1]
6x + 7y = -29 [Equation 2]
A. (1, - 5)
B. (1, 5)
C. (- 1, 5)
D. (- 1, - 5)

Solutions

Step: 1

y = x - 6

[Rearrange Equation 1.]

Step: 2

6x + 7(x - 6) = -29

[Substitute the values.]

Step: 3

13x - 42 = -29

[Group the like terms.]

Step: 4

13x = 13

[Add 42 to both sides of the equation.]

Step: 5

x = 1

[Divide throughout by 13.]

Step: 6

y = x - 6 = 1 - 6

[Substitute the values.]

Step: 7

y = - 5

[Simplify.]

Step: 8

The solution for the linear system is (1, - 5).

Correct Answer is : (1, - 5)

Q11Which of the following ordered pairs satisfies the linear system?
5x - y = 0 [Equation 1]
x - 3y = 0 [Equation 2]
A. (0, 0)
B. (-5, 3)
C. (5, 3)
D. (5, -3)

Solutions

Step: 1

y = 5x

[Rearrange Equation 1.]

Step: 2

x - 3(5x) = 0

[Substitute the values.]

Step: 3

-14x = 0

[Group the like terms.]

Step: 4

x = 0

[Divide throughout by -14.]

Step: 5

y = 5x = 5(0)

[Substitute the values.]

Step: 6

y = 0

[Simplify.]

Step: 7

The solution for the linear system is (0, 0).

Correct Answer is : (0, 0)

Q12Which of the following ordered pairs satisfies the linear system?
4x - 8y = 8 [Equation 1.]
- x + 6y = -18 [Equation 2.]
A. (- 6, - 4)
B. (- 7, 0)
C. (- 7, - 4)
D. (0, 4)

Solutions

Step: 1

- x + 6y = -18

Step: 2

x = 18 + 6y

[Rearrange equation 2.]

Step: 3

4(18 + 6y) - 8y = 8

[Substitute the values.]

Step: 4

16y + 72 = 8

[Group the like terms.]

Step: 5

16y = -64

[Subtract 72 from the two sides of the equation.]

Step: 6

y = - 4

[Divide throughout by 16.]

Step: 7

x = 18 + 6y = 18 + 6(- 4)

[Substitute the values.]

Step: 8

x = - 6

[Simplify.]

Step: 9

The solution for the linear system is (- 6, - 4).

Correct Answer is : (- 6, - 4)

Q13Which of the following ordered pairs satisfies the linear system?
-x + y = 6 [Equation 1]
3x - 2y = 2 [Equation 2]
A. (14, 20)
B. (14, -20)
C. (-14, -20)
D. (-14, 20)

Solutions

Step: 1

y = x + 6

[Rearrange Equation 1.]

Step: 2

3x - 2(x + 6) = 2

[Substitute the values.]

Step: 3

x - 12 = 2

[Group the like terms.]

Step: 4

x = 14

[Add 12 to both sides of the equation.]

Step: 5

y = 14 + 6

[Substitute the values.]

Step: 6

y = 20

[Simplify.]

Step: 7

The solution for the linear system is (14, 20).

Correct Answer is : (14, 20)

Q14Solve the linear system.
5x + 3y = 21
x - 3y = 3
A. (0, - 13)
B. (- 4, 13)
C. (4, 0)
D. (4, 13)

Solutions

Step: 1

5x + 3y = 21

[Equation 1.]

Step: 2

x - 3y = 3

[Equation 2.]

Step: 3

x = 3y + 3

[Rearrange equation 2.]

Step: 4

5(3y + 3) + 3y = 21

[Substitute the values.]

Step: 5

18y + 15 = 21

[Group the like terms.]

Step: 6

18y = 6

[Subtract 15 from the two sides of the equation.]

Step: 7

y = 13

[Divide throughout by 18.]

Step: 8

x = 3y + 3 = 3(13) + 3

[Substitute the value in step 3.]

Step: 9

x = 4

[Simplify.]

Step: 10

The solution for the linear system is (4, 13).

Correct Answer is : (4, 13)

Q15Which of the following ordered pairs satisfies the linear system?
4x + 3y = 16 [Equation 1]
-x + 5y = 19 [Equation 2]
A. (-1, 4)
B. (-1, -4)
C. (1, -4)
D. (1, 4)

Solutions

Step: 1

x = 5y - 19

[Rearrange Equation 2.]

Step: 2

4(5y - 19) + 3y = 16

[Substitute the values.]

Step: 3

23y - 76 = 16

[Group the like terms.]

Step: 4

23y = 92

[Add 76 to both sides of the equation.]

Step: 5

y = 4

[Divide throughout by 23.]

Step: 6

x = 5y - 19 = 5(4) - 19

[Substitute the values.]

Step: 7

x = 1

[Simplify.]

Step: 8

The solution for the linear system is (1, 4).

Correct Answer is : (1, 4)

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

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