Question

Solve the system below using SUBSTITUTION. Show step-by-step work to earn credit. Use the Formula Editor x−−√ to type math or use the Image icon to upload a photo of your work.

2x+2y=38
y=x+3

Answer 1

To solve the system of equations using substitution, we have the following two equations:

1. \( 2x + 2y = 38 \)
2. \( y = x + 3 \)

### Step 1: Substitute \( y \) in the first equation

We can use the second equation to substitute \( y \) in the first equation.

Substituting \( y \) in equation 1:

\[
2x + 2(x + 3) = 38
\]

### Step 2: Simplify the equation

Now, we will simplify the left side of the equation:

\[
2x + 2x + 6 = 38
\]

Combine like terms:

\[
4x + 6 = 38
\]

### Step 3: Solve for \( x \)

Next, subtract 6 from both sides:

\[
4x = 38 - 6
\]
\[
4x = 32
\]

Now, divide both sides by 4:

\[
x = \frac{32}{4}
\]
\[
x = 8
\]

### Step 4: Substitute \( x \) back to find \( y \)

Now that we have \( x \), we can substitute \( x = 8 \) back into the second equation to find \( y \):

\[
y = x + 3
\]
\[
y = 8 + 3
\]
\[
y = 11
\]

### Step 5: Write the solution

The solution to the system of equations is:

\[
(x, y) = (8, 11)
\]

### Step 6: Verify the solution

To ensure the solution is correct, we can substitute \( x = 8 \) and \( y = 11 \) back into the original equations.

For the first equation:

\[
2(8) + 2(11) = 16 + 22 = 38 \quad \text{(True)}
\]

For the second equation:

\[
11 = 8 + 3 \quad \text{(True)}
\]

Both equations are satisfied, confirming that the solution is correct.

Thus, the solution is:

\[
\boxed{(8, 11)}
\]