Question

-7x - 2y = -13
x - 2y = 11

Explanation:

Step1: Label the equations

Equation 1: $-7x - 2y = -13$
Equation 2: $x - 2y = 11$

Step2: Eliminate $y$ via subtraction

Subtract Equation 2 from Equation 1 to remove the $-2y$ term.
$$(-7x - 2y) - (x - 2y) = -13 - 11$$
$$-7x - 2y - x + 2y = -24$$
$$-8x = -24$$

Step3: Solve for $x$

Divide both sides by $-8$ to isolate $x$.
$$x = \frac{-24}{-8} = 3$$

Step4: Substitute $x=3$ into Equation 2

Plug $x=3$ into Equation 2 to solve for $y$.
$$3 - 2y = 11$$

Step5: Solve for $y$

Rearrange and isolate $y$.
$$-2y = 11 - 3$$
$$-2y = 8$$
$$y = \frac{8}{-2} = -4$$

Answer:

$x=3$, $y=-4$