Explore IDNLearn.com's extensive Q&A database and find the answers you need. Our platform is designed to provide quick and accurate answers to any questions you may have.

What should be the first step in adding these equations to eliminate [tex]y[/tex]?

[tex]\[
\begin{array}{l}
8x + 3y = 2 \\
4x - 6y = -7 \\
\end{array}
\][/tex]

A. Multiply the top equation by 2.

B. Multiply the bottom equation by 8.

C. Multiply the top equation by 4.

D. Multiply the bottom equation by 2.


Sagot :

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.