A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{aligned} 5 x-2 y & =-29 \\ -5 x-5 y & =85 \end{aligned}$ $\newline$ 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{aligned} 5 x-2 y & =-29 \\ -5 x-5 y & =85 \end{aligned}

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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 Variables: Analyze the system of equations to determine which variable can be eliminated with the least amount of work. $\newline$ We have the system of equations: $\newline$ $5x - 2y = -29$ $\newline$ $-5x - 5y = 85$ $\newline$ To eliminate a variable, we look for coefficients that are opposites or the same. Here, the coefficients of $x$ in both equations are $5$ and $-5$ , which are opposites.
Decide Elimination Operation: Decide on the operation to use for elimination. $\newline$ Since the coefficients of $x$ are opposites ( $5$ and $-5$ ), we can add the two equations together to eliminate $x$ .
Perform Operation: Perform the chosen operation to check if it eliminates the chosen variable. $\newline$ Adding the two equations: $\newline$ $(5x - 2y) + (-5x - 5y) = -29 + 85$ $\newline$ $5x - 5x - 2y - 5y = 56$ $\newline$ $0x - 7y = 56$ $\newline$ This operation eliminates $x$ , as expected.