Solving Systems of Equations by Substitution Worksheet for 8th ... - Free Printable

Let’s solve each system of equations using substitution. We’ll go one by one, carefully.

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Problem 1:
> y = x + 2
> -2x + 3y = 6

Substitute y = x + 2 into the second equation:

-2x + 3(x + 2) = 6
→ -2x + 3x + 6 = 6
→ x + 6 = 6
→ x = 0

Now plug x = 0 into y = x + 2 → y = 0 + 2 = 2

✔ Solution: (0, 2)

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Problem 2:
> 2x + 3y = 5
> x = 4y - 3

Substitute x = 4y - 3 into first equation:

2(4y - 3) + 3y = 5
→ 8y - 6 + 3y = 5
→ 11y - 6 = 5
→ 11y = 11
→ y = 1

Then x = 4(1) - 3 = 1

✔ Solution: (1, 1)

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Problem 3:
> y = 3x + 5
> 4x - y = -5

Substitute y = 3x + 5 into second equation:

4x - (3x + 5) = -5
→ 4x - 3x - 5 = -5
→ x - 5 = -5
→ x = 0

Then y = 3(0) + 5 = 5

✔ Solution: (0, 5)

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Problem 4:
> 4x - 2y = 2
> x = 3y - 17

Substitute x = 3y - 17 into first equation:

4(3y - 17) - 2y = 2
→ 12y - 68 - 2y = 2
→ 10y - 68 = 2
→ 10y = 70
→ y = 7

Then x = 3(7) - 17 = 21 - 17 = 4

✔ Solution: (4, 7)

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Problem 5:
> x = -2
> 4x + 2y = 10

We already know x = -2. Plug into second equation:

4(-2) + 2y = 10
→ -8 + 2y = 10
→ 2y = 18
→ y = 9

✔ Solution: (-2, 9)

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Problem 6:
> x + 2y = 7
> -5x - 2y = -11

Wait — this is not set up for direct substitution yet. Let’s solve one equation for a variable.

From first equation: x = 7 - 2y

Plug into second equation:

-5(7 - 2y) - 2y = -11
→ -35 + 10y - 2y = -11
→ -35 + 8y = -11
→ 8y = 24
→ y = 3

Then x = 7 - 2(3) = 7 - 6 = 1

✔ Solution: (1, 3)

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Problem 7:
> -4x + y = 6
> -5x + y = 21

Solve first equation for y: y = 4x + 6

Plug into second equation:

-5x + (4x + 6) = 21
→ -5x + 4x + 6 = 21
→ -x + 6 = 21
→ -x = 15
→ x = -15

Then y = 4(-15) + 6 = -60 + 6 = -54

✔ Solution: (-15, -54)

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Problem 8:
> -7x + 2y = -15
> x - 2y = 15

Solve second equation for x: x = 2y + 15

Plug into first equation:

-7(2y + 15) + 2y = -15
→ -14y - 105 + 2y = -15
→ -12y - 105 = -15
→ -12y = 90
→ y = -90/12 = -15/2 = -7.5

Then x = 2(-7.5) + 15 = -15 + 15 = 0

✔ Solution: (0, -7.5) or (0, -15/2)

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Problem 9:
> -6x + y = -2
> -3x + y = -12

Solve first equation for y: y = 6x - 2

Plug into second equation:

-3x + (6x - 2) = -12
→ 3x - 2 = -12
→ 3x = -10
→ x = -10/3

Then y = 6(-10/3) - 2 = -20 - 2 = -22

✔ Solution: (-10/3, -22)

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Problem 10:
> -6x + y = -2
> 3x - 8y = 28

Solve first equation for y: y = 6x - 2

Plug into second equation:

3x - 8(6x - 2) = 28
→ 3x - 48x + 16 = 28
→ -45x + 16 = 28
→ -45x = 12
→ x = -12/45 = -4/15

Then y = 6(-4/15) - 2 = -24/15 - 30/15 = -54/15 = -18/5

✔ Solution: (-4/15, -18/5)

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Final Answer:
1. (0, 2)
2. (1, 1)
3. (0, 5)
4. (4, 7)
5. (-2, 9)
6. (1, 3)
7. (-15, -54)
8. (0, -7.5)
9. (-10/3, -22)
10. (-4/15, -18/5)