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'll follow these steps systematically. The given equations are:

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

### Step 1: Substitute Equation 2 into Equation 1

Since Equation 2 expresses \( y \) in terms of \( x \), we can substitute \( y \) in Equation 1:

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

### Step 2: Simplify the equation

Now, distribute the \( 2 \) on the left side:

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

Combine like terms:

\[
4x + 6 = 38
\]

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

Next, subtract \( 6 \) from both sides:

\[
4x = 38 - 6
\]

\[
4x = 32
\]

Now, divide by \( 4 \):

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

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

Now that we have \( x \), we can use Equation 2 to find \( y \):

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

### Step 5: State the solution

The solution to the system of equations is:

\[
x = 8, \quad y = 11
\]

### Step 6: Write the final answer

Thus, the solution in coordinate form is:

\[
(8, 11)
\]

### Verification

To verify, we can insert \( x = 8 \) and \( y = 11 \) back into the original equations:

1. For \( 2x + 2y = 38 \):

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

2. For \( y = x + 3 \):

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

Both equations check out. Therefore, our solution \( (8, 11) \) is correct.