A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{aligned} -2 x+7 y & =64 \\ 9 x+7 y & =20 \end{aligned}$ $\newline$ Subtract to eliminate $\mathbf{x}$ . $\newline$ Add to eliminate $\mathbf{y}$ . $\newline$ Subtract to eliminate $\mathbf{y}$ . $\newline$ Add 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} -2 x+7 y & =64 \\ 9 x+7 y & =20 \end{aligned}

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Subtract to eliminate

\mathbf{x}

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Add to eliminate

\mathbf{y}

\newline

Subtract to eliminate

\mathbf{y}

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Add to eliminate

\mathbf{x}

Analyze Variables: Analyze the system of equations to determine which variable can be eliminated by addition or subtraction. $\newline$ We have the system of equations: $\newline$ $-2x + 7y = 64$ $\newline$ $9x + 7y = 20$ $\newline$ To eliminate a variable, we look for coefficients that are the same or opposites. Here, the coefficients of $y$ are the same in both equations.
Choose Operation: Decide on the operation to use for elimination. $\newline$ Since the coefficients of $y$ are the same ( $7$ and $7$ ), we can eliminate $y$ by subtracting one equation from the other.
Verify Decision: Perform a quick check to ensure no math error has been made in the decision process. The coefficients of $y$ are indeed the same, and subtraction is the correct operation to eliminate $y$ .