To eliminate [tex]\( y \)[/tex] from the system of equations
[tex]\[
\begin{array}{r}
3x + 4y = 8 \\
6x - 2y = 9 \\
\end{array}
\][/tex]
our goal is to make the coefficients of [tex]\( y \)[/tex] in both equations equal in magnitude but opposite in sign.
The coefficients of [tex]\( y \)[/tex] are [tex]\( 4 \)[/tex] in the first equation and [tex]\(-2 \)[/tex] in the second equation. To make these coefficients equal (but opposite in sign), we can multiply the second equation by [tex]\( 2 \)[/tex]. When we do this, the coefficient of [tex]\( y \)[/tex] in the second equation will become [tex]\( -4 \)[/tex], which is opposite (in sign) to the [tex]\( 4y \)[/tex] in the first equation.
Thus, the first step is to multiply the bottom equation by [tex]\( 2 \)[/tex]:
[tex]\[
\begin{array}{r}
3x + 4y = 8 \\
2 \cdot (6x - 2y) = 2 \cdot 9 \\
\end{array}
\][/tex]
[tex]\[
\begin{array}{r}
3x + 4y = 8 \\
12x - 4y = 18 \\
\end{array}
\][/tex]
So, the correct answer is:
A. Multiply the bottom equation by 2.
