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
4

$x$ + 9

$y$ = -28

A.

$2, - 4$
B.

$2, 4$
C.

$- 2, 4$
D.

$- 2, - 4$

Solutions

Step: 1

$y$ =

$x$ - 6

[Rearrange Equation 1.]

Step: 2

$x$ + 9(

$x$ - 6) = -28

[Substitute

$y$ = (

$x$ - 6) in equation 2.]

Step: 3

$x$ - 54 = -28

[Combine like terms.]

Step: 4

$x$ = 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?
2

$x$ -

$y$ = 0

$x$ - 4

$y$ = 0

A.

$0, 0$
B.

$2, - 4$
C.

$- 2, 4$
D.

$2, 4$

Solutions

Step: 1

$y$ = 2

$x$

[Rearrange Equation 1.]

Step: 2

$x$ - 4(2

$x$ ) = 0

[Substitute

$y$ = 2

$x$ in Equation 2.]

Step: 3

- 7

$x$ = 0

[Combine like terms.]

Step: 4

$x$ = 0

[Divide each side by - 7.]

Step: 5

$y$ = 2

$x$ = 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?
5

$x$ - 3

$y$ = -3
-

$x$ + 3

$y$ = -21
A.

$- 6, - 9$
B.

$6, 6$
C.

$-28, -52$
D.

$6, 5$

Solutions

Step: 1

$x$ + 3

$y$ = -21

[Original equation 2.]

Step: 2

$x$ = 21 + 3

$y$

[Revise equation 2.]

Step: 3

5(21 + 3

$y$ ) - 3

$y$ = -3

[Replace

$x$ with 21 + 3

$y$ in Equation 1.]

Step: 4

$y$ + 105 = -3

[Combine like terms.]

Step: 5

$y$ = -108

[Subtract 105 from each side.]

Step: 6

$y$ = - 9

[Divide each side by 12.]

Step: 7

$x$ = 21 + 3

$y$ = 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
6

$x$ - 5

$y$ = -31
A.

$9, 17$
B.

$- 9, 17$
C.

$9, - 17$
D.

$- 9, - 17$

Solutions

Step: 1

$y$ =

$x$ + 8

[Rearrange Equation 1.]

Step: 2

$x$ - 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.
5

$x$ + 3

$y$ = 21

$x$ - 3

$y$ = 3

A. (4,

$13$ )
B. (4,

$- 13$ )
C. (- 4,

$- 13$ )
D. (- 4,

$13$ )

Solutions

Step: 1

$x$ + 3

$y$ = 21

[Equation 1.]

Step: 2

$x$ - 3

$y$ = 3

[Equation 2.]

Step: 3

$x$ = 3

$y$ + 3

[Revised Equation 2.]

Step: 4

5(3

$y$ + 3) + 3

$y$ = 21

[Substitute

$x$ = 3

$y$ + 3 in Equation 1.]

Step: 5

$y$ + 15 = 21

[Combine like terms.]

Step: 6

$y$ = 6

[Subtract 15 from each side.]

Step: 7

$y$ =

$13$

[Divide each side by 18.]

Step: 8

$x$ = 3

$y$ + 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?
4

$x$ + 3

$y$ = 17
-

$x$ + 3

$y$ = 7
A.

$- 2, 3$
B.

$- 2, - 3$
C.

$2, - 3$
D.

$2, 3$

Solutions

Step: 1

$x$ + 3

$y$ = 17 .....

$1$
-

$x$ + 3

$y$ = 7 .....

$2$

Step: 2

Equation 2 can be rearranged as

$x$ = 3

$y$ - 7 so that

$x$ in equation 1 can be replaced with this in order to solve the linear system.

Step: 3

4(3

$y$ - 7) + 3

$y$ = 17

[Replace

$x$ with 3

$y$ - 7 in Equation 1.]

Step: 4

$y$ - 28 = 17

[Combine like terms.]

Step: 5

$y$ = 45

[Add 28 to both sides.]

Step: 6

$y$ = 3

[Divide each side by 15.]

Step: 7

$x$ = 3

$y$ - 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?
- 16

$x$ + 3

$y$ = -97

$x$ -

$y$ = 2
A.

$7, 5$
B.

$- 7, - 5$
C.

$7, - 5$
D.

$- 7, 5$

Solutions

Step: 1

- 16

$x$ + 3

$y$ = -97 - - - - - - - -

$1$

Step: 2

$x$ -

$y$ = 2 - - - - - - - -

$2$

Step: 3

$x$ =

$y$ + 2

[Rearrange Equation 2.]

Step: 4

- 16(

$y$ + 2) + 3

$y$ = -97

[Substitute

$y$ + 2 for

$x$ in Equation 1.]

Step: 5

- 13

$y$ - 32 = -97

[Combine like terms.]

Step: 6

- 13

$y$ = -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:
6

$x$ - 3

$y$ = 15
- 4

$x$ + 2

$y$ = - 10
A. No solution
B.

$3, 0$
C. Infinite solutions
D.

$2, 5$

Solutions

Step: 1

$x$ - 3

$y$ = 15

[First equation.]

Step: 2

- 3

$y$ = 15 - 6

$x$

[Subtract 6

$x$ from the two sides of the equation.]

Step: 3

$y$ = - 5 + 2

$x$

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

Step: 4

- 4

$x$ + 2

$y$ = - 10

[Second equation.]

Step: 5

- 4

$x$ + 2(- 5 + 2

$x$ ) = - 10

[Substitute the values.]

Step: 6

- 4

$x$ - 10 + 4

$x$ = - 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:
2

$x$ + 12

$y$ = 10
6

$x$ = - 36

$y$ + 36

A.

$36, 0$
B.

$6, 6$
C. Infinite solution
D. No solution

Solutions

Step: 1

$x$ = - 36

$y$ + 36

[Second equation.]

Step: 2

$x$ = - 6

$y$ + 6

[Divide throughout by 6 .]

Step: 3

$x$ + 12

$y$ = 10

[First equation.]

Step: 4

2(- 6

$y$ + 6) + 12

$y$ = 10

[Substitute the values.]

Step: 5

- 12

$y$ + 12 + 12

$y$ = 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]
6

$x$ + 7

$y$ = -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

$x$ + 7(

$x$ - 6) = -29

[Substitute the values.]

Step: 3

$x$ - 42 = -29

[Group the like terms.]

Step: 4

$x$ = 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?
5

$x$ -

$y$ = 0 [Equation 1]

$x$ - 3

$y$ = 0 [Equation 2]
A.

$0, 0$
B.

$-5, 3$
C.

$5, 3$
D.

$5, -3$

Solutions

Step: 1

$y$ = 5

$x$

[Rearrange Equation 1.]

Step: 2

$x$ - 3(5

$x$ ) = 0

[Substitute the values.]

Step: 3

-14

$x$ = 0

[Group the like terms.]

Step: 4

$x$ = 0

[Divide throughout by -14.]

Step: 5

$y$ = 5

$x$ = 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?
4

$x$ - 8

$y$ = 8 [Equation 1.]
-

$x$ + 6

$y$ = -18 [Equation 2.]
A.

$- 6, - 4$
B.

$- 7, 0$
C.

$- 7, - 4$
D.

$0, 4$

Solutions

Step: 1

$x$ + 6

$y$ = -18

Step: 2

$x$ = 18 + 6

$y$

[Rearrange equation 2.]

Step: 3

4(18 + 6

$y$ ) - 8

$y$ = 8

[Substitute the values.]

Step: 4

$y$ + 72 = 8

[Group the like terms.]

Step: 5

$y$ = -64

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

Step: 6

$y$ = - 4

[Divide throughout by 16.]

Step: 7

$x$ = 18 + 6

$y$ = 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]
3

$x$ - 2

$y$ = 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

$x$ - 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.
5

$x$ + 3

$y$ = 21

$x$ - 3

$y$ = 3
A. (0, -

$13$ )
B. (- 4,

$13$ )
C.

$4, 0$
D. (4,

$13$ )

Solutions

Step: 1

$x$ + 3

$y$ = 21

[Equation 1.]

Step: 2

$x$ - 3

$y$ = 3

[Equation 2.]

Step: 3

$x$ = 3

$y$ + 3

[Rearrange equation 2.]

Step: 4

5(3

$y$ + 3) + 3

$y$ = 21

[Substitute the values.]

Step: 5

$y$ + 15 = 21

[Group the like terms.]

Step: 6

$y$ = 6

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

Step: 7

$y$ =

$13$

[Divide throughout by 18.]

Step: 8

$x$ = 3

$y$ + 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?
4

$x$ + 3

$y$ = 16 [Equation 1]
-

$x$ + 5

$y$ = 19 [Equation 2]
A.

$-1, 4$
B.

$-1, -4$
C.

$1, -4$
D.

$1, 4$

Solutions

Step: 1

$x$ = 5

$y$ - 19

[Rearrange Equation 2.]

Step: 2

4(5

$y$ - 19) + 3

$y$ = 16

[Substitute the values.]

Step: 3

$y$ - 76 = 16

[Group the like terms.]

Step: 4

$y$ = 92

[Add 76 to both sides of the equation.]

Step: 5

$y$ = 4

[Divide throughout by 23.]

Step: 6

$x$ = 5

$y$ - 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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