Question

1. $-2x - 6y = -26$; $-2x + y = -12$

Explanation:

Step1: Subtract the two equations to eliminate \(x\)

We have the system of equations:
\[

$$\begin{cases} -2x - 6y = -26 \quad (1)\\ -2x + y = -12 \quad (2) \end{cases}$$

\]
Subtract equation \((2)\) from equation \((1)\):
\[

$$\begin{align*} (-2x - 6y) - (-2x + y) &= -26 - (-12)\\ -2x - 6y + 2x - y &= -26 + 12\\ -7y &= -14 \end{align*}$$

\]

Step2: Solve for \(y\)

Divide both sides of \(-7y = -14\) by \(-7\):
\[
y=\frac{-14}{-7} = 2
\]

Step3: Substitute \(y = 2\) into equation \((2)\) to solve for \(x\)

Substitute \(y = 2\) into \(-2x + y = -12\):
\[

$$\begin{align*} -2x + 2 &= -12\\ -2x &= -12 - 2\\ -2x &= -14\\ x&=\frac{-14}{-2}=7 \end{align*}$$

\]

Answer:

The solution to the system is \(x = 7\) and \(y = 2\)