A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{aligned} 2 x+8 y & =-2 \\ -2 x+9 y & =-32 \end{aligned}$ $\newline$ Add to eliminate $\mathbf{y}$ . $\newline$ Subtract to eliminate $\mathbf{y}$ . $\newline$ Add to eliminate $\mathbf{x}$ . $\newline$ 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} 2 x+8 y & =-2 \\ -2 x+9 y & =-32 \end{aligned}

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Add to eliminate

\mathbf{y}

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Subtract to eliminate

\mathbf{y}

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Add to eliminate

\mathbf{x}

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Subtract to eliminate

\mathbf{x}

Identify Variable for Elimination: Analyze the system of equations to determine which variable can be easily eliminated. $\newline$ We have the system of equations: $\newline$ $2x + 8y = -2$ $\newline$ $-2x + 9y = -32$ $\newline$ To eliminate a variable, we look for coefficients that are opposites or the same. Here, the coefficients of $x$ are $2$ and $-2$ , which are opposites.
Choose Elimination Operation: Decide on the operation to use for elimination. Since the coefficients of $x$ are already opposites ( $2$ and $-2$ ), we can add the two equations together to eliminate the $x$ variable.
Perform Check for Accuracy: Perform a quick check to ensure no math error has been made in the decision process. $\newline$ Adding the equations: $\newline$ $(2x + 8y) + (-2x + 9y) = -2 + (-32)$ $\newline$ The $x$ terms will cancel out, and we will be left with an equation in $y$ only.