Question

-8x - 4y = -8
x + 2y = 13
(□, □)
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Explanation:

Step1: Simplify the first equation

Divide the first equation \(-8x - 4y = -8\) by \(-4\) to simplify.
\(\frac{-8x}{-4}-\frac{4y}{-4}=\frac{-8}{-4}\)
Which gives \(2x + y = 2\). Let's call this Equation (1).

Step2: Solve the second equation for x

From the second equation \(x + 2y = 13\), we can express \(x\) as \(x = 13 - 2y\). Let's call this Equation (2).

Step3: Substitute Equation (2) into Equation (1)

Substitute \(x = 13 - 2y\) into \(2x + y = 2\):
\(2(13 - 2y)+y = 2\)
Expand the left side: \(26 - 4y + y = 2\)
Combine like terms: \(26 - 3y = 2\)

Step4: Solve for y

Subtract 26 from both sides: \(-3y = 2 - 26\)
\(-3y = -24\)
Divide both sides by \(-3\): \(y=\frac{-24}{-3}=8\)

Step5: Substitute y = 8 into Equation (2) to find x

Substitute \(y = 8\) into \(x = 13 - 2y\):
\(x = 13 - 2\times8\)
\(x = 13 - 16\)
\(x = -3\)

Answer:

\((-3, 8)\)