Solving Systems of Equations by Substitution Worksheets - Math Monks - Free Printable

Let’s solve each system of equations by substitution. We’ll go one at a time, step by step.

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Problem ①:
y = 6x - 11
-2x - 3y = -7

Step 1: Since the first equation already gives y in terms of x, substitute “6x - 11” for y in the second equation.

→ -2x - 3(6x - 11) = -7

Step 2: Distribute the -3:

→ -2x - 18x + 33 = -7

Step 3: Combine like terms:

→ -20x + 33 = -7

Step 4: Subtract 33 from both sides:

→ -20x = -40

Step 5: Divide by -20:

→ x = 2

Step 6: Plug x = 2 into the first equation to find y:

→ y = 6(2) - 11 = 12 - 11 = 1

✔ Solution: (2, 1)

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Problem ②:
x + 3y = 6
2x + 8y = -12

Step 1: Solve the first equation for x:

→ x = 6 - 3y

Step 2: Substitute into the second equation:

→ 2(6 - 3y) + 8y = -12

Step 3: Distribute:

→ 12 - 6y + 8y = -12

Step 4: Combine like terms:

→ 12 + 2y = -12

Step 5: Subtract 12:

→ 2y = -24

Step 6: Divide by 2:

→ y = -12

Step 7: Plug back into x = 6 - 3y:

→ x = 6 - 3(-12) = 6 + 36 = 42

✔ Solution: (42, -12)

Wait — let’s double-check that. If y = -12 and x = 42, plug into original equations:

First: 42 + 3(-12) = 42 - 36 = 6 ✔️
Second: 2(42) + 8(-12) = 84 - 96 = -12 ✔️

Okay, correct.

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Problem ③:
x + 3y = 12
2x + y = 6

Step 1: Solve first equation for x:

→ x = 12 - 3y

Step 2: Substitute into second equation:

→ 2(12 - 3y) + y = 6

Step 3: Distribute:

→ 24 - 6y + y = 6

Step 4: Combine:

→ 24 - 5y = 6

Step 5: Subtract 24:

→ -5y = -18

Step 6: Divide by -5:

→ y = 18/5 = 3.6

Hmm, fraction? Let’s keep it as fraction: y = 18/5

Step 7: Find x:

x = 12 - 3*(18/5) = 12 - 54/5 = 60/5 - 54/5 = 6/5

✔ Solution: (6/5, 18/5) or (1.2, 3.6)

Check:

First: 6/5 + 3*(18/5) = 6/5 + 54/5 = 60/5 = 12 ✔️
Second: 2*(6/5) + 18/5 = 12/5 + 18/5 = 30/5 = 6 ✔️

Good.

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Problem ④:
y = -2x - 9
y = -5x - 21

Since both equal y, set them equal:

→ -2x - 9 = -5x - 21

Add 5x to both sides:

→ 3x - 9 = -21

Add 9:

→ 3x = -12

Divide by 3:

→ x = -4

Plug into either equation, say first:

y = -2(-4) - 9 = 8 - 9 = -1

✔ Solution: (-4, -1)

Check with second: y = -5(-4) -21 = 20 - 21 = -1 ✔️

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Problem ⑤:
-2x + 4y = -16
y = x - 2

Substitute y = x - 2 into first equation:

→ -2x + 4(x - 2) = -16

Distribute:

→ -2x + 4x - 8 = -16

Combine:

→ 2x - 8 = -16

Add 8:

→ 2x = -8

Divide by 2:

→ x = -4

Then y = -4 - 2 = -6

✔ Solution: (-4, -6)

Check: -2(-4) + 4(-6) = 8 - 24 = -16 ✔️

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Problem ⑥:
2x - 3y = -1
y = x - 1

Substitute y = x - 1 into first equation:

→ 2x - 3(x - 1) = -1

Distribute:

→ 2x - 3x + 3 = -1

Combine:

→ -x + 3 = -1

Subtract 3:

→ -x = -4 → x = 4

Then y = 4 - 1 = 3

✔ Solution: (4, 3)

Check: 2(4) - 3(3) = 8 - 9 = -1 ✔️

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Problem ⑦:
y = 2x - 15
y = 5x

Set equal:

→ 2x - 15 = 5x

Subtract 2x:

→ -15 = 3x

Divide by 3:

→ x = -5

Then y = 5*(-5) = -25

✔ Solution: (-5, -25)

Check: y = 2(-5) -15 = -10 -15 = -25 ✔️

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Problem ⑧:
2x + 4y = 4
y = x - 2

Substitute y = x - 2 into first equation:

→ 2x + 4(x - 2) = 4

Distribute:

→ 2x + 4x - 8 = 4

Combine:

→ 6x - 8 = 4

Add 8:

→ 6x = 12

Divide by 6:

→ x = 2

Then y = 2 - 2 = 0

✔ Solution: (2, 0)

Check: 2(2) + 4(0) = 4 + 0 = 4 ✔️

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Final Answer:

① (2, 1)
② (42, -12)
③ (6/5, 18/5) or (1.2, 3.6)
④ (-4, -1)
⑤ (-4, -6)
⑥ (4, 3)
⑦ (-5, -25)
⑧ (2, 0)