A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{aligned} -8 x+7 y & =30 \\ 4 x-7 y & =-22 \end{aligned}$ $\newline$ Add to eliminate $\mathbf{x}$ . $\newline$ Subtract to eliminate $\mathbf{y}$ . $\newline$ Add to eliminate $\mathbf{y}$ . $\newline$ Subtract to eliminate $\mathbf{x}$ .

Full solution

Q. A variable needs to be eliminated to solve the system of equations below. Choose the correct first step.

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\begin{aligned} -8 x+7 y & =30 \\ 4 x-7 y & =-22 \end{aligned}

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Add to eliminate

\mathbf{x}

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Subtract to eliminate

\mathbf{y}

\newline

Add to eliminate

\mathbf{y}

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Subtract to eliminate

\mathbf{x}

Identify Opposite Coefficients: We have the system of equations: $\newline$ $-8x + 7y = 30$ $\newline$ $4x - 7y = -22$ $\newline$ To eliminate a variable, we look for coefficients that are opposites or can be made into opposites. Here, we notice that the coefficients of $y$ are $7$ and $-7$ , which are already opposites.
Add Equations to Eliminate $y$ : Since the coefficients of $y$ are opposites, we can add the two equations together to eliminate $y$ . The addition will result in the $y$ terms canceling each other out. $\newline$ $(-8x + 7y) + (4x - 7y) = 30 + (-22)$
Perform Addition and Simplify: Performing the addition, we get: $\newline$ $-8x + 4x + 7y - 7y = 30 - 22$ $\newline$ $-4x = 8$ $\newline$ This shows that adding the two equations eliminates $y$ .