Question

1. -3x - y = -2

-2x + y = -8

Explanation:

Step1: Add the two equations to eliminate \( y \)

We have the system of equations:
\[

$$\begin{cases} -3x - y = -2 \\ -2x + y = -8 \end{cases}$$

\]
Adding the left - hand sides and the right - hand sides of the two equations:
\((-3x - y)+(-2x + y)=-2+(-8)\)
Simplify the left - hand side: \(-3x - y-2x + y=-5x\)
Simplify the right - hand side: \(-2-8 = - 10\)
So we get the equation \(-5x=-10\)

Step2: Solve for \( x \)

Divide both sides of the equation \(-5x=-10\) by \(-5\):
\(x=\frac{-10}{-5}=2\)

Step3: Substitute \( x = 2 \) into one of the original equations to solve for \( y \)

Let's substitute \( x = 2 \) into the first equation \(-3x - y=-2\)
We have \(-3\times2-y=-2\)
Simplify: \(-6 - y=-2\)
Add 6 to both sides: \(-y=-2 + 6=4\)
Multiply both sides by \(-1\): \(y=-4\)

Answer:

The solution to the system of equations is \(x = 2\) and \(y=-4\)