To solve the system of equations using the substitution method, follow these steps:
Given the system:
[tex]\[
\begin{array}{l}
2x + 2y = 16 \\
y = x - 4
\end{array}
\][/tex]
Step 1: Solve one of the equations for one variable.
The second equation is already solved for [tex]\( y \)[/tex]:
[tex]\[
y = x - 4
\][/tex]
Step 2: Substitute the expression from Step 1 into the other equation.
Substitute [tex]\( y = x - 4 \)[/tex] into the first equation:
[tex]\[
2x + 2(x - 4) = 16
\][/tex]
Step 3: Simplify and solve for [tex]\( x \)[/tex].
Simplify the equation:
[tex]\[
2x + 2x - 8 = 16
\][/tex]
Combine like terms:
[tex]\[
4x - 8 = 16
\][/tex]
Add 8 to both sides of the equation:
[tex]\[
4x = 24
\][/tex]
Divide both sides by 4:
[tex]\[
x = 6
\][/tex]
Step 4: Substitute [tex]\( x \)[/tex] back into the expression found in Step 1 to find [tex]\( y \)[/tex].
Substitute [tex]\( x = 6 \)[/tex] into [tex]\( y = x - 4 \)[/tex]:
[tex]\[
y = 6 - 4
\][/tex]
Simplify:
[tex]\[
y = 2
\][/tex]
Step 5: Write the solution as an ordered pair.
The solution to the system is:
[tex]\[
(x, y) = (6, 2)
\][/tex]
Step 6: Match the solution with the given choices.
The correct ordered pair from the choices is:
[tex]\[
\text{A. } (6, 2)
\][/tex]
So, the correct answer is [tex]\(\boxed{A}\)[/tex].
