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Which of these shows the result of using the first equation to substitute for [tex]$y$[/tex] in the second equation, then combining like terms?

[tex]\[
\begin{array}{l}
y = 2x \\
2x + 3y = 16
\end{array}
\][/tex]

A. [tex]\(8x = 16\)[/tex]
B. [tex]\(5y = 16\)[/tex]
C. [tex]\(5x = 16\)[/tex]
D. [tex]\(4x = 16\)[/tex]


Sagot :

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]