#### 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)

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
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)

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)

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)

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
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)

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)

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
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)

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
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)

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

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
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)

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)

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)

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)

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)

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)

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)