Question

solve the system of equations $x + y = -12$ and $-8x + 7y = 6$ by combining the equations.
$\square \

$$\begin{pmatrix} x + y = -12 \\\\ -8x + 7y = 6 \\end{pmatrix}$$

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$$\begin{aligned} x + y &= -12 \\\\ -8x + 7y &= 6 \\\\ \\hline \\square x + \\square y &= \\square \\end{aligned}$$

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Explanation:

Step1: Eliminate $x$ variable

Multiply first equation by 8:
$8(x + y) = 8(-12) \implies 8x + 8y = -96$

Step2: Add to second equation

Add new equation to $-8x + 7y = 6$:
$$(8x + 8y) + (-8x + 7y) = -96 + 6$$

Step3: Simplify to solve for $y$

Combine like terms:
$15y = -90 \implies y = \frac{-90}{15} = -6$

Step4: Substitute $y$ to find $x$

Plug $y=-6$ into $x + y = -12$:
$x + (-6) = -12 \implies x = -12 + 6 = -6$

Answer:

$x=-6$, $y=-6$

To fill the given blanks for combining equations:
Multiply the first equation by 8, so the top blank is 8, bottom blank is 1.
Adding gives: $0x + 15y = -90$