A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{aligned} -3 x+4 y & =52 \\ 7 x-4 y & =-84 \end{aligned}$ $\newline$ Subtract to eliminate $\mathbf{y}$ . $\newline$ Subtract to eliminate $\mathbf{x}$ . $\newline$ Add to eliminate $\mathbf{x}$ . $\newline$ 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.

\newline

\begin{aligned} -3 x+4 y & =52 \\ 7 x-4 y & =-84 \end{aligned}

\newline

Subtract to eliminate

\mathbf{y}

\newline

Subtract to eliminate

\mathbf{x}

\newline

Add to eliminate

\mathbf{x}

\newline

Add to eliminate

\mathbf{y}

Given Equations: We are given the system of equations: $\newline$ $-3x + 4y = 52$ $\newline$ $7x - 4y = -84$ $\newline$ To eliminate a variable, we look for coefficients that are opposites or can be made into opposites. Here, the coefficients of $y$ are $4$ and $-4$ , which are already opposites.
Eliminate Variable: Since the coefficients of $y$ are opposites, we can add the two equations together to eliminate $y$ . The addition will result in the $y$ terms canceling each other out. $(-3x + 4y) + (7x - 4y) = 52 + (-84)$
Add Equations: Performing the addition, we get: $\newline$ $-3x + 7x + 4y - 4y = 52 - 84$
Perform Addition: Simplifying the equation, we get: $4x = -32$
Simplify Equation: We have successfully eliminated the variable $y$ by adding the two equations. The next steps would involve solving for $x$ , but since the question only asks for the correct first step to eliminate a variable, we have our answer.