To solve this problem, let's follow the steps to use the first equation to substitute for [tex]\( y \)[/tex] in the second equation and then combine like terms.
Given equations:
[tex]\[
\begin{array}{l}
y = 2x \\
2x + 3y = 16
\end{array}
\][/tex]
1. Substitute [tex]\( y = 2x \)[/tex] from the first equation into the second equation:
[tex]\[
2x + 3(2x) = 16
\][/tex]
2. Simplify by distributing the [tex]\( 3 \)[/tex] through the [tex]\( 2x \)[/tex] inside the parentheses:
[tex]\[
2x + 6x = 16
\][/tex]
3. Combine like terms (both [tex]\( 2x \)[/tex] and [tex]\( 6x \)[/tex] are terms involving [tex]\( x \)[/tex]):
[tex]\[
8x = 16
\][/tex]
Therefore, the correct result after substituting for [tex]\( y \)[/tex] and combining like terms is:
[tex]\[
\boxed{8x = 16}
\][/tex]
The correct answer is:
A. [tex]\( 8x = 16 \)[/tex]
