Question

-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: $-7x-2y - x + 2y=-8x$, and the right - hand side: $-24$. So we get $-8x=-24$.

Step2: Solve for x

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

Step3: Substitute x = 3 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 of the system of equations is $x = 3,y=-4$