Question

-7x - y = 1\
-7x + y = -13\
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Explanation:

Step1: Identify the system of equations

We have the system:
\[

$$\begin{cases} -7x - y = 1 \\ -7x + y = -13 \end{cases}$$

\]

Step2: Add the two equations to eliminate \(y\)

Adding the left - hand sides and the right - hand sides of the two equations:
\((-7x - y)+(-7x + y)=1+(-13)\)
Simplify the left - hand side: \(-7x - y-7x + y=-14x\)
Simplify the right - hand side: \(1-13 = - 12\)
So we get the equation \(-14x=-12\)

Step3: Solve for \(x\)

Divide both sides of the equation \(-14x=-12\) by \(-14\):
\(x=\frac{-12}{-14}=\frac{6}{7}\)

Step4: Substitute \(x = \frac{6}{7}\) into the first equation to solve for \(y\)

Substitute \(x=\frac{6}{7}\) into \(-7x - y = 1\):
\(-7\times\frac{6}{7}-y = 1\)
Simplify \(-7\times\frac{6}{7}\): \(-6 - y=1\)
Add \(y\) to both sides: \(-6=1 + y\)
Subtract \(1\) from both sides: \(y=-6 - 1=-7\)

Answer:

The solution of the system of equations \(

$$\begin{cases}-7x - y = 1\\-7x + y=-13\end{cases}$$

\) is \(x = \frac{6}{7}\) and \(y=-7\)