Question

solve using elimination.
x + 2y = -9
-2x - y = -6
(□, □)

Explanation:

Step1: Multiply first equation by 2

To eliminate \(x\), we multiply the first equation \(x + 2y=-9\) by 2. This gives us \(2x + 4y=-18\).

Step2: Add new equation to second equation

Now we add the new equation \(2x + 4y=-18\) to the second equation \(-2x - y=-6\).
\[

$$\begin{align*} (2x + 4y)+(-2x - y)&=-18+(-6)\\ 2x + 4y-2x - y&=-24\\ 3y&=-24 \end{align*}$$

\]

Step3: Solve for \(y\)

Divide both sides of \(3y = - 24\) by 3: \(y=\frac{-24}{3}=-8\)

Step4: Substitute \(y\) into first equation

Substitute \(y = - 8\) into \(x + 2y=-9\): \(x+2\times(-8)=-9\)
\[

$$\begin{align*} x-16&=-9\\ x&=-9 + 16\\ x&=7 \end{align*}$$

\]

Answer:

\((7, - 8)\)