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

Let’s solve each system step by step using substitution. We’ll go one problem at a time.

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Problem 1:

Equations:
- x = -2y
- x - y = 9

Since the first equation already gives us x in terms of y, we can substitute “-2y” for x in the second equation.

Substitute into second equation:
(-2y) - y = 9
→ -3y = 9
→ y = -3

Now plug y = -3 back into x = -2y:
x = -2*(-3) = 6

✔ Solution: (6, -3)

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Problem 2:

Equations:
- y = x - 4
- -4x - 6y = -16

Substitute y = x - 4 into the second equation:

-4x - 6(x - 4) = -16
→ -4x -6x + 24 = -16
→ -10x + 24 = -16
→ -10x = -40
→ x = 4

Now find y: y = 4 - 4 = 0

✔ Solution: (4, 0)

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Problem 3:

Equations:
- -x - 3y = -18
- y = -4x + 6

Substitute y = -4x + 6 into the first equation:

-x - 3(-4x + 6) = -18
→ -x + 12x - 18 = -18
→ 11x - 18 = -18
→ 11x = 0
→ x = 0

Now find y: y = -4(0) + 6 = 6

✔ Solution: (0, 6)

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Problem 4:

Equations:
- -2x + 2y = 6
- 4x + 2y = -5

We need to solve one equation for one variable. Let’s solve the first equation for y.

From -2x + 2y = 6:
Add 2x to both sides:
2y = 2x + 6
Divide by 2:
y = x + 3

Now substitute y = x + 3 into the second equation:

4x + 2(x + 3) = -5
→ 4x + 2x + 6 = -5
→ 6x + 6 = -5
→ 6x = -11
→ x = -11/6

Now find y: y = (-11/6) + 3 = (-11/6) + (18/6) = 7/6

✔ Solution: (-11/6, 7/6)

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Problem 5:

Equations:
- y = -6
- 3x - 6y = 30

Substitute y = -6 into the second equation:

3x - 6(-6) = 30
→ 3x + 36 = 30
→ 3x = -6
→ x = -2

✔ Solution: (-2, -6)

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Problem 6:

Equations:
- -2x - y = -5
- x - 8y = -23

Solve the first equation for y:

-2x - y = -5
→ -y = 2x - 5
→ y = -2x + 5

Now substitute into second equation:

x - 8(-2x + 5) = -23
→ x + 16x - 40 = -23
→ 17x - 40 = -23
→ 17x = 17
→ x = 1

Now find y: y = -2(1) + 5 = 3

✔ Solution: (1, 3)

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Problem 7:

Equations:
- 2x + y = 2
- 3x + 7y = 14

Solve first equation for y:

y = 2 - 2x

Substitute into second equation:

3x + 7(2 - 2x) = 14
→ 3x + 14 - 14x = 14
→ -11x + 14 = 14
→ -11x = 0
→ x = 0

Now find y: y = 2 - 2(0) = 2

✔ Solution: (0, 2)

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Problem 8:

Equations:
- y = 4x - 9
- y = x - 3

Since both equal y, set them equal to each other:

4x - 9 = x - 3
→ 4x - x = -3 + 9
→ 3x = 6
→ x = 2

Now find y: y = 2 - 3 = -1
(or check with other: y = 4*2 - 9 = 8 - 9 = -1 → same)

✔ Solution: (2, -1)

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Final Answer:
1) (6, -3)
2) (4, 0)
3) (0, 6)
4) (-11/6, 7/6)
5) (-2, -6)
6) (1, 3)
7) (0, 2)
8) (2, -1)