Question

solve using elimination.
-x - 9y = -6
-5x + 4y = 19
(\square, \square)
submit

Explanation:

Step1: Multiply first equation by -5

To eliminate \(x\), we multiply the first equation \(-x - 9y=-6\) by \(-5\). This gives us \(5x + 45y = 30\).

Step2: Add to second equation

Now we add this new equation \(5x + 45y = 30\) to the second equation \(-5x + 4y = 19\).
\[

$$\begin{align*} (5x + 45y)+(-5x + 4y)&=30 + 19\\ 5x-5x+45y + 4y&=49\\ 49y&=49 \end{align*}$$

\]

Step3: Solve for y

Divide both sides of \(49y = 49\) by \(49\).
\[
y=\frac{49}{49}=1
\]

Step4: Substitute y into first equation

Substitute \(y = 1\) into the first original equation \(-x-9y=-6\).
\[

$$\begin{align*} -x-9(1)&=-6\\ -x - 9&=-6 \end{align*}$$

\]

Step5: Solve for x

Add 9 to both sides: \(-x=-6 + 9=3\). Multiply both sides by \(-1\) to get \(x=-3\).

Answer:

\((-3, 1)\)