Question

8x + 7y = -1\
x - y = -17\
(\boxed{\quad})(\boxed{\quad})\
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Explanation:

Step1: Rewrite the system of equations

We have the system of equations:
\[

$$\begin{cases} 8x + 7y=- 1\\ x - y=-17 \end{cases}$$

\]
From the second equation \(x - y=-17\), we can express \(x\) in terms of \(y\) as \(x=y - 17\).

Step2: Substitute \(x=y - 17\) into the first equation

Substitute \(x=y - 17\) into \(8x + 7y=-1\):
\[

$$\begin{align*} 8(y - 17)+7y&=-1\\ 8y-136 + 7y&=-1\\ 15y-136&=-1 \end{align*}$$

\]

Step3: Solve for \(y\)

Add 136 to both sides of the equation \(15y-136=-1\):
\[

$$\begin{align*} 15y-136 + 136&=-1 + 136\\ 15y&=135 \end{align*}$$

\]
Divide both sides by 15:
\[
y=\frac{135}{15}=9
\]

Step4: Solve for \(x\)

Substitute \(y = 9\) into \(x=y - 17\):
\[
x=9-17=-8
\]

Answer:

\(x=-8\), \(y = 9\)