Question

Use the substitution method to solve the system of equations. Choose the correct ordered pair.
2x + 2y= 16
y= x-4
• A. (6, -2)
• в. (2,2)
C. (6,2)
D. (2, -2)

Answer 1

To solve the system of equations using the substitution method, we'll start with the two equations:

1. \( 2x + 2y = 16 \)
2. \( y = x - 4 \)

We can substitute the expression for \( y \) from the second equation into the first equation.

1. Substitute \( y \) in the first equation:

\[
2x + 2(x - 4) = 16
\]

2. Simplify this equation:

\[
2x + 2x - 8 = 16
\]
\[
4x - 8 = 16
\]

3. Add 8 to both sides:

\[
4x = 24
\]

4. Divide by 4:

\[
x = 6
\]

5. Now substitute \( x = 6 \) back into the second equation to find \( y \):

\[
y = 6 - 4 = 2
\]

The solution to the system of equations is \( (x, y) = (6, 2) \).

Thus, the correct ordered pair is:

**C. (6, 2)**