Question

solve using elimination.
$2x + y = -2$
$x + 2y = -16$
$(square, square)$

Explanation:

Step1: Eliminate x by multiplying the second equation by 2

Multiply the equation \(x + 2y = -16\) by 2 to get \(2x + 4y = -32\).

Step2: Subtract the first equation from the new equation

Subtract \(2x + y = -2\) from \(2x + 4y = -32\):
\[

$$\begin{align*} (2x + 4y) - (2x + y) &= -32 - (-2)\\ 2x + 4y - 2x - y &= -32 + 2\\ 3y &= -30 \end{align*}$$

\]

Step3: Solve for y

Divide both sides by 3: \(y = \frac{-30}{3} = -10\).

Step4: Substitute y into the first equation to solve for x

Substitute \(y = -10\) into \(2x + y = -2\):
\[

$$\begin{align*} 2x + (-10) &= -2\\ 2x - 10 &= -2\\ 2x &= -2 + 10\\ 2x &= 8\\ x &= \frac{8}{2} = 4 \end{align*}$$

\]

Answer:

(4, -10)