Question

Solve the system of equations below using substitution. You must show all work to earn full credit. y=2x+4 3x+2y=22

Answer 1

To solve the system of equations using substitution, we'll follow these steps:

1. Write down the two equations:
\[
y = 2x + 4 \quad \text{(1)}
\]
\[
3x + 2y = 22 \quad \text{(2)}
\]

2. Substitute equation (1) into equation (2). Since \( y \) is expressed in terms of \( x \) in equation (1), we can replace \( y \) in equation (2) with \( 2x + 4 \):
\[
3x + 2(2x + 4) = 22
\]

3. Now, simplify the equation:
\[
3x + 4x + 8 = 22
\]

4. Combine the like terms:
\[
7x + 8 = 22
\]

5. Now, isolate \( x \) by subtracting 8 from both sides:
\[
7x = 22 - 8
\]
\[
7x = 14
\]

6. Divide both sides by 7:
\[
x = 2
\]

7. Now that we have the value of \( x \), we can find \( y \) using equation (1):
\[
y = 2(2) + 4
\]
\[
y = 4 + 4
\]
\[
y = 8
\]

8. Thus, the solution to the system of equations is:
\[
(x, y) = (2, 8)
\]

**Final Answer:**
\[
x = 2, \quad y = 8
\]