Question

1. $-7x - 2y = -13$

$x - 2y = 11$

Explanation:

Step1: Subtract the two equations

We have the system of equations:

$$\begin{cases}-7x - 2y = -13 \\ x - 2y = 11\end{cases}$$

Subtract the second equation from the first equation:
$$(-7x - 2y) - (x - 2y) = -13 - 11$$
Simplify the left - hand side:
$$-7x - 2y - x + 2y=-8x$$
Simplify the right - hand side:
$$-24$$
So we get the equation \(-8x=-24\)

Step2: Solve for x

Divide both sides of the equation \(-8x = - 24\) by \(-8\):
\(x=\frac{-24}{-8}=3\)

Step3: Substitute x into one of the original equations to solve for y

Substitute \(x = 3\) into the second equation \(x-2y = 11\):
\(3-2y=11\)
Subtract 3 from both sides:
\(-2y=11 - 3=8\)
Divide both sides by \(-2\):
\(y=\frac{8}{-2}=-4\)

Answer:

The solution to the system of equations is \(x = 3,y=-4\)