A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{array}{l} -9 x+5 y=11 \\ -9 x+2 y=-1 \end{array}$ $\newline$ Add to eliminate $\mathbf{x}$ . $\newline$ Subtract to eliminate $\mathbf{x}$ . $\newline$ Subtract to eliminate $\mathbf{y}$ . $\newline$ Add 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} -9 x+5 y=11 \\ -9 x+2 y=-1 \end{array}

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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}

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Add to eliminate

\mathbf{y}

Analyze Variables for Elimination: Analyze the system of equations to determine which variable can be eliminated by addition or subtraction. $\newline$ The system of equations is: $\newline$ $-9x + 5y = 11$ $\newline$ $-9x + 2y = -1$ $\newline$ We can see that the coefficients of $x$ in both equations are the same ( $-9$ ) and the coefficients of $y$ ( $5$ and $2$ ) are different. To eliminate $x$ , we can add the two equations together because the coefficients of $x$ are identical and will cancel each other out.
Perform Addition to Eliminate x: Perform the addition of the two equations to check if x is eliminated. $\newline$ $(-9x + 5y) + (-9x + 2y) = 11 + (-1)$ $\newline$ $-9x - 9x + 5y + 2y = 10$ $\newline$ $-18x + 7y = 10$ $\newline$ This step shows that adding the equations does not eliminate x because we did not consider the signs of the coefficients correctly. We made a math error.