A variable needs to be eliminated to solve the system of equations below. Choose the correct first step. $\newline$ $\begin{aligned} -10 x-y & =-30 \\ 10 x+2 y & =40 \end{aligned}$ $\newline$ Subtract to eliminate $\mathbf{y}$ . $\newline$ Subtract to eliminate $\mathbf{x}$ . $\newline$ Add 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} -10 x-y & =-30 \\ 10 x+2 y & =40 \end{aligned}

\newline

Subtract to eliminate

\mathbf{y}

\newline

Subtract to eliminate

\mathbf{x}

\newline

Add to eliminate

\mathbf{y}

\newline

Add to eliminate

\mathbf{x}

Given System of Equations: We are given the system of equations: $\{-10x - y = -30, 10x + 2y = 40\}$ To eliminate a variable, we look for coefficients that are opposites or can be made into opposites. Here, we notice that the coefficients of $x$ in both equations are $-10$ and $10$ , which are already opposites.
Identifying Opposite Coefficients: Since the coefficients of $x$ are opposites, we can add the two equations together to eliminate the $x$ variable. This is because $(-10x) + (10x)$ equals $0$ , effectively removing the $x$ variable from the equation.
Eliminating x Variable: Let's add the two equations: $\newline$ $(-10x - y) + (10x + 2y) = -30 + 40$ $\newline$ $-10x + 10x - y + 2y = 10$ $\newline$ $0x + y = 10$ $\newline$ This simplifies to $y = 10$ .