Systems Of Equations: Substitution #1 Worksheet - Free Printable

Let's solve each system of equations using substitution, step by step, and verify the answers provided in the answer key.

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1.

Equations:
- $ y = 6 $
- $ -x + y = 2 $

Step 1: Substitute $ y = 6 $ into the second equation:
$ -x + 6 = 2 $
$ -x = 2 - 6 = -4 $
$ x = 4 $

✔ Solution: $ (4, 6) $ — matches the answer key.

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2.

Equations:
- $ x = 5 $
- $ 3x - 2y = 9 $

Step 1: Substitute $ x = 5 $ into the second equation:
$ 3(5) - 2y = 9 $
$ 15 - 2y = 9 $
$ -2y = -6 $
$ y = 3 $

✔ Solution: $ (5, 3) $ — matches.

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3.

Equations:
- $ 4x = -8 $
- $ 2x + 5y = 6 $

Step 1: Solve first equation:
$ 4x = -8 \Rightarrow x = -2 $

Step 2: Plug $ x = -2 $ into second equation:
$ 2(-2) + 5y = 6 $
$ -4 + 5y = 6 $
$ 5y = 10 $
$ y = 2 $

✔ Solution: $ (-2, 2) $ — matches.

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4.

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

Step 1: Substitute $ y = -5x $ into second equation:
$ 6x + (-5x) = 2 $
$ x = 2 $

Then $ y = -5(2) = -10 $

✔ Solution: $ (2, -10) $ — matches.

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5.

Equations:
- $ x = 9y $
- $ 3y - 3x = 24 $

Step 1: Substitute $ x = 9y $ into second equation:
$ 3y - 3(9y) = 24 $
$ 3y - 27y = 24 $
$ -24y = 24 $
$ y = -1 $

Then $ x = 9(-1) = -9 $

✔ Solution: $ (-9, -1) $ — matches.

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6.

Equations:
- $ y - x = -8 $
- $ 2x - 16 = y $

Step 1: From second equation: $ y = 2x - 16 $

Substitute into first equation:
$ (2x - 16) - x = -8 $
$ x - 16 = -8 $
$ x = 8 $

Then $ y = 2(8) - 16 = 16 - 16 = 0 $

✔ Solution: $ (8, 0) $ — matches.

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7.

Equations:
- $ y = 3x + 1 $
- $ y = 8x - 4 $

Step 1: Set equations equal since both equal $ y $:
$ 3x + 1 = 8x - 4 $
$ 1 + 4 = 8x - 3x $
$ 5 = 5x $
$ x = 1 $

Then $ y = 3(1) + 1 = 4 $

✔ Solution: $ (1, 4) $ — matches.

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8.

Equations:
- $ x + y = 0 $
- $ 5x + 4y = 6 $

Step 1: From first equation: $ y = -x $

Substitute into second:
$ 5x + 4(-x) = 6 $
$ 5x - 4x = 6 $
$ x = 6 $

Then $ y = -6 $

✔ Solution: $ (6, -6) $ — matches.

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9.

Equations:
- $ 2y = -2x + 6 $
- $ x - 5y = -15 $

Step 1: Simplify first equation:
Divide by 2: $ y = -x + 3 $

Now substitute into second equation:
$ x - 5(-x + 3) = -15 $
$ x + 5x - 15 = -15 $
$ 6x - 15 = -15 $
$ 6x = 0 $
$ x = 0 $

Then $ y = -0 + 3 = 3 $

✔ Solution: $ (0, 3) $ — matches.

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10.

Equations:
- $ 5x + y = 2 $
- $ 20x + 3y = -4 $

Step 1: Solve first for $ y $:
$ y = 2 - 5x $

Substitute into second:
$ 20x + 3(2 - 5x) = -4 $
$ 20x + 6 - 15x = -4 $
$ 5x + 6 = -4 $
$ 5x = -10 $
$ x = -2 $

Then $ y = 2 - 5(-2) = 2 + 10 = 12 $

✔ Solution: $ (-2, 12) $ — matches.

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11.

Equations:
- $ -8x + 2y = -14 $
- $ 4x - 6y = 22 $

Step 1: Let’s solve one equation for one variable. Use first:

Solve for $ y $:
$ -8x + 2y = -14 $
$ 2y = 8x - 14 $
$ y = 4x - 7 $

Now substitute into second equation:
$ 4x - 6(4x - 7) = 22 $
$ 4x - 24x + 42 = 22 $
$ -20x + 42 = 22 $
$ -20x = -20 $
$ x = 1 $

Then $ y = 4(1) - 7 = -3 $

✔ Solution: $ (1, -3) $ — matches.

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12.

Equations:
- $ 2x + 4y = -18 $
- $ 5x - 10y = -5 $

Step 1: Solve first equation for $ x $:
$ 2x = -18 - 4y $
$ x = -9 - 2y $

Substitute into second equation:
$ 5(-9 - 2y) - 10y = -5 $
$ -45 - 10y - 10y = -5 $
$ -45 - 20y = -5 $
$ -20y = 40 $
$ y = -2 $

Then $ x = -9 - 2(-2) = -9 + 4 = -5 $

✔ Solution: $ (-5, -2) $ — matches.

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✔ Final Answer:

All solutions match the answer key provided.

Each system was solved correctly using substitution, and the given answers are accurate.

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🔍 Summary of Method:

- Step 1: Solve one equation for one variable.
- Step 2: Substitute that expression into the other equation.
- Step 3: Solve for the remaining variable.
- Step 4: Back-substitute to find the other variable.
- Step 5: Write as an ordered pair.

This worksheet is well-designed and all answers are correct! 🎉