Substitution Method Worksheet featuring six problems with linear equations to solve using the substitution method.

Let's solve each system of equations using the substitution method, as indicated in the worksheet. The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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1)

$$
\begin{align*}
2x + 8y &= 20 \\
y &= 2
\end{align*}
$$

Step 1: Since $ y = 2 $, substitute this into the first equation:

$$
2x + 8(2) = 20 \\
2x + 16 = 20 \\
2x = 4 \\
x = 2
$$

✔ Solution: $ x = 2, y = 2 $

---

2)

$$
\begin{align*}
x &= 5 \\
2x + y &= 10
\end{align*}
$$

Step 1: Substitute $ x = 5 $ into the second equation:

$$
2(5) + y = 10 \\
10 + y = 10 \\
y = 0
$$

✔ Solution: $ x = 5, y = 0 $

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3)

$$
\begin{align*}
5x - 2y &= 3 \\
y &= 2x
\end{align*}
$$

Step 1: Substitute $ y = 2x $ into the first equation:

$$
5x - 2(2x) = 3 \\
5x - 4x = 3 \\
x = 3
$$

Now find $ y $:
$ y = 2x = 2(3) = 6 $

✔ Solution: $ x = 3, y = 6 $

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4)

$$
\begin{align*}
2y + x &= -15 \\
x &= 3y
\end{align*}
$$

Step 1: Substitute $ x = 3y $ into the first equation:

$$
2y + (3y) = -15 \\
5y = -15 \\
y = -3
$$

Now find $ x $:
$ x = 3(-3) = -9 $

✔ Solution: $ x = -9, y = -3 $

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5)

$$
\begin{align*}
4x + 7y &= 19 \\
y &= x + 9
\end{align*}
$$

Step 1: Substitute $ y = x + 9 $ into the first equation:

$$
4x + 7(x + 9) = 19 \\
4x + 7x + 63 = 19 \\
11x + 63 = 19 \\
11x = -44 \\
x = -4
$$

Now find $ y $:
$ y = (-4) + 9 = 5 $

✔ Solution: $ x = -4, y = 5 $

---

6)

$$
\begin{align*}
y &= 6x + 11 \\
2y - 4x &= 14
\end{align*}
$$

Step 1: Substitute $ y = 6x + 11 $ into the second equation:

$$
2(6x + 11) - 4x = 14 \\
12x + 22 - 4x = 14 \\
8x + 22 = 14 \\
8x = -8 \\
x = -1
$$

Now find $ y $:
$ y = 6(-1) + 11 = -6 + 11 = 5 $

✔ Solution: $ x = -1, y = 5 $

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✔ Final Answers:

1) $ x = 2, y = 2 $
2) $ x = 5, y = 0 $
3) $ x = 3, y = 6 $
4) $ x = -9, y = -3 $
5) $ x = -4, y = 5 $
6) $ x = -1, y = 5 $

Let me know if you'd like these checked or graphed!