A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{aligned} -2 x-10 y & =0 \\ 6 x-10 y & =80 \end{aligned}$ $\newline$ Subtract to eliminate $\mathbf{x}$ . $\newline$ Add to eliminate $\mathbf{y}$ . $\newline$ Subtract to eliminate $\mathbf{y}$ . $\newline$ Add 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.

\newline

\begin{aligned} -2 x-10 y & =0 \\ 6 x-10 y & =80 \end{aligned}

\newline

Subtract to eliminate

\mathbf{x}

\newline

Add to eliminate

\mathbf{y}

\newline

Subtract to eliminate

\mathbf{y}

\newline

Add to eliminate

\mathbf{x}

Given System of Equations: We are given the system of equations: $\{-2x - 10y = 0, 6x - 10y = 80\}$ To eliminate a variable, we need to look for coefficients that are the same or opposites. Here, the coefficients of $y$ are the same in both equations ( $-10y$ and $-10y$ ). Therefore, we can eliminate $y$ by adding the two equations together.
Eliminating a Variable: Let's add the two equations: $\newline$ $(-2x - 10y) + (6x - 10y) = 0 + 80$ $\newline$ Combining like terms, we get: $\newline$ $(-2x + 6x) + (-10y - 10y) = 80$ $\newline$ $4x + 0y = 80$
Adding Equations: Since the $y$ terms have been eliminated, we are left with an equation in one variable: $\newline$ $4x = 80$ $\newline$ This confirms that adding the two equations was the correct first step to eliminate $y$ .