Printable worksheet for practicing solving systems of linear equations using substitution.

Let’s solve each system step by step using substitution. I’ll go one problem at a time, carefully checking my work.

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Problem 1:

Equations:
(1) y = -4x + 16
(2) -3x + 8y = 23

Substitute equation (1) into equation (2):

-3x + 8(-4x + 16) = 23
→ -3x -32x + 128 = 23
→ -35x + 128 = 23
→ -35x = 23 - 128 = -105
→ x = (-105)/(-35) = 3

Now plug x = 3 into equation (1):
y = -4(3) + 16 = -12 + 16 = 4

✔ Check in equation (2): -3(3) + 8(4) = -9 + 32 = 23 → Correct.

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Problem 2:

Equations:
(1) -3x + 6y = -24
(2) y = 7x + 22

Substitute equation (2) into equation (1):

-3x + 6(7x + 22) = -24
→ -3x + 42x + 132 = -24
→ 39x + 132 = -24
→ 39x = -24 - 132 = -156
→ x = -156 / 39 = -4

Plug x = -4 into equation (2):
y = 7(-4) + 22 = -28 + 22 = -6

✔ Check in equation (1): -3(-4) + 6(-6) = 12 - 36 = -24 → Correct.

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Problem 3:

Equations:
(1) y = 5x + 5
(2) y = x + 5

Set them equal since both equal y:

5x + 5 = x + 5
→ 5x - x = 5 - 5
→ 4x = 0
→ x = 0

Plug into equation (2): y = 0 + 5 = 5

✔ Check in equation (1): y = 5(0)+5 = 5 → Correct.

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Problem 4:

Equations:
(1) y = 4x + 22
(2) y = -4x - 18

Set equal:

4x + 22 = -4x - 18
→ 4x + 4x = -18 - 22
→ 8x = -40
→ x = -5

Plug into equation (1): y = 4(-5) + 22 = -20 + 22 = 2

✔ Check in equation (2): y = -4(-5) -18 = 20 - 18 = 2 → Correct.

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Problem 5:

Equations:
(1) x - 3y = -12
(2) 4x + 6y = -12

Solve equation (1) for x:
x = 3y - 12

Substitute into equation (2):

4(3y - 12) + 6y = -12
→ 12y - 48 + 6y = -12
→ 18y - 48 = -12
→ 18y = 36
→ y = 2

Then x = 3(2) - 12 = 6 - 12 = -6

✔ Check in equation (2): 4(-6) + 6(2) = -24 + 12 = -12 → Correct.

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Problem 6:

Equations:
(1) 2x - 5y = 22
(2) x + 5y = -4

Solve equation (2) for x:
x = -4 - 5y

Substitute into equation (1):

2(-4 - 5y) - 5y = 22
→ -8 -10y -5y = 22
→ -8 -15y = 22
→ -15y = 30
→ y = -2

Then x = -4 -5(-2) = -4 + 10 = 6

✔ Check in equation (1): 2(6) -5(-2) = 12 + 10 = 22 → Correct.

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Problem 7:

Equations:
(1) y = -4
(2) -3x -6y = 15

Since y is already given, plug y = -4 into equation (2):

-3x -6(-4) = 15
→ -3x + 24 = 15
→ -3x = 15 - 24 = -9
→ x = 3

✔ Check: -3(3) -6(-4) = -9 + 24 = 15 → Correct.

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Problem 8:

Equations:
(1) 2x + 4y = -10
(2) 7x + 8y = -23

Solve equation (1) for x:

2x = -10 - 4y
→ x = (-10 - 4y)/2 = -5 - 2y

Substitute into equation (2):

7(-5 - 2y) + 8y = -23
→ -35 -14y + 8y = -23
→ -35 -6y = -23
→ -6y = 12
→ y = -2

Then x = -5 -2(-2) = -5 + 4 = -1

✔ Check in equation (1): 2(-1) + 4(-2) = -2 -8 = -10 → Correct.
Check in equation (2): 7(-1) + 8(-2) = -7 -16 = -23 → Correct.

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Final Answer:

1) x = 3, y = 4
2) x = -4, y = -6
3) x = 0, y = 5
4) x = -5, y = 2
5) x = -6, y = 2
6) x = 6, y = -2
7) x = 3, y = -4
8) x = -1, y = -2