To solve the system of equations using the substitution method, follow these steps:
Given equations:
[tex]\[
\begin{array}{l}
16x - 2y = 74 \\
2x - 2y = 4
\end{array}
\][/tex]
Step 1: Solve one of the equations for one variable in terms of the other. Let’s solve the second equation for [tex]\(y\)[/tex].
Equation 2:
[tex]\[
2x - 2y = 4
\][/tex]
Divide by 2 to simplify:
[tex]\[
x - y = 2
\][/tex]
Rearrange to solve for [tex]\(y\)[/tex]:
[tex]\[
y = x - 2
\][/tex]
Step 2: Substitute this expression for [tex]\(y\)[/tex] into the first equation.
First Equation:
[tex]\[
16x - 2y = 74
\][/tex]
Substitute [tex]\(y = x - 2\)[/tex] into the first equation:
[tex]\[
16x - 2(x - 2) = 74
\][/tex]
Step 3: Distribute and simplify:
[tex]\[
16x - 2x + 4 = 74
\][/tex]
Combine like terms:
[tex]\[
14x + 4 = 74
\][/tex]
Step 4: Isolate [tex]\(x\)[/tex]:
[tex]\[
14x = 70
\][/tex]
Step 5: Solve for [tex]\(x\)[/tex]:
[tex]\[
x = 5
\][/tex]
Step 6: Substitute [tex]\(x = 5\)[/tex] back into the expression we found for [tex]\(y\)[/tex]:
[tex]\[
y = x - 2
\][/tex]
[tex]\[
y = 5 - 2
\][/tex]
[tex]\[
y = 3
\][/tex]
Step 7: Write the solution as an ordered pair:
[tex]\[
(x, y) = (5, 3)
\][/tex]
Therefore, the correct ordered pair is:
[tex]\[
\boxed{D. (5,3)}
\][/tex]
