Question

-8x - 7y = 12
-7x - 7y = 7
(□, □)

Explanation:

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

We have the system:

$$
LATEXBLOCK0
$$

Subtract the second equation from the first equation:

$$ (-8x - 7y) - (-7x - 7y) = 12 - 7 $$

Simplify the left - hand side:

$$ -8x - 7y + 7x + 7y=-x $$

Simplify the right - hand side: \( 12 - 7 = 5 \)
So, we get \( -x=5 \), which implies \( x=- 5 \)

Step2: Substitute \( x = - 5 \) into one of the original equations to find \( y \)

Let's substitute \( x=-5 \) into the second equation \( -7x - 7y = 7 \)

$$ -7\times(-5)-7y = 7 $$

First, calculate \( -7\times(-5)=35 \)
The equation becomes \( 35-7y = 7 \)
Subtract 35 from both sides:

$$ -7y=7 - 35 $$

$$ -7y=-28 $$

Divide both sides by - 7:

$$ y=\frac{-28}{-7}=4 $$

Answer:

\((-5,4)\)