The goal is to eliminate [tex]\(y\)[/tex] by adding the two given equations together. Here are the equations:
[tex]\[
\begin{array}{l}
8x + 3y = 2 \\
4x - 6y = -7 \\
\end{array}
\][/tex]
To eliminate [tex]\(y\)[/tex], the coefficients of [tex]\(y\)[/tex] in both equations should be opposites.
1. The coefficient of [tex]\(y\)[/tex] in the first equation is 3.
2. The coefficient of [tex]\(y\)[/tex] in the second equation is -6.
If we multiply the entire first equation by 2, we will get the coefficient of [tex]\(y\)[/tex] in the first equation to be 6, which is the opposite of -6.
The first equation, when multiplied by 2, becomes:
[tex]\[
2(8x + 3y) = 2(2) \implies 16x + 6y = 4
\][/tex]
Now, we have:
[tex]\[
\begin{array}{l}
16x + 6y = 4 \\
4x - 6y = -7 \\
\end{array}
\][/tex]
Adding these two equations together will now eliminate [tex]\(y\)[/tex]:
[tex]\[
(16x + 6y) + (4x - 6y) = 4 + (-7) \implies 20x = -3
\][/tex]
Therefore, the first step in adding these equations to eliminate [tex]\(y\)[/tex] is:
A. Multiply the top equation by 2.
