A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{array}{l} -3 x+7 y=61 \\ -9 x-7 y=-13 \end{array}$ $\newline$ Add to eliminate $\mathbf{y}$ . $\newline$ Add to eliminate $\mathbf{x}$ . $\newline$ Subtract to eliminate $\mathbf{x}$ . $\newline$ Subtract to eliminate $\mathbf{y}$ .

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{array}{l} -3 x+7 y=61 \\ -9 x-7 y=-13 \end{array}

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Add to eliminate

\mathbf{y}

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Add to eliminate

\mathbf{x}

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Subtract to eliminate

\mathbf{x}

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Subtract to eliminate

\mathbf{y}

Analyze Coefficients: Analyze the coefficients of $x$ and $y$ in both equations. $\newline$ The first equation is $-3x + 7y = 61$ . $\newline$ The second equation is $-9x - 7y = -13$ . $\newline$ To eliminate a variable, we look for coefficients that are the same or opposites. $\newline$ Here, the coefficients of $y$ are $7$ and $-7$ , which are opposites.
Decide Variable to Eliminate: Decide which variable to eliminate. Since the coefficients of $y$ are opposites, adding the two equations will eliminate $y$ .
Perform Addition: Perform the addition to check if y is eliminated. $\newline$ Adding the two equations: $\newline$ $(-3x + 7y) + (-9x - 7y) = 61 + (-13)$ $\newline$ The y terms cancel out: $\newline$ $-3x - 9x = 61 - 13$
Simplify Resulting Equation: Simplify the resulting equation to confirm that $y$ has been eliminated. $-12x = 48$ This confirms that by adding the two equations, $y$ is eliminated.