Question

1. $-8x - 8y = -24$ $-x + 4y = -23$

Explanation:

Step1: Simplify the first equation

Divide the first equation \(-8x - 8y = -24\) by \(-8\) to simplify it.
\(\frac{-8x}{-8}+\frac{-8y}{-8}=\frac{-24}{-8}\)
Which simplifies to \(x + y = 3\), and we can rewrite it as \(x = 3 - y\).

Step2: Substitute \(x\) into the second equation

The second equation is \(-x + 4y = -23\). Substitute \(x = 3 - y\) into this equation.
\(-(3 - y)+4y=-23\)
Expand the left - hand side: \(-3 + y+4y=-23\)
Combine like terms: \(-3 + 5y=-23\)

Step3: Solve for \(y\)

Add 3 to both sides of the equation \(-3 + 5y=-23\):
\(5y=-23 + 3\)
\(5y=-20\)
Divide both sides by 5: \(y=\frac{-20}{5}=-4\)

Step4: Solve for \(x\)

Substitute \(y = - 4\) into \(x = 3 - y\):
\(x=3-(-4)=3 + 4 = 7\)

Answer:

The solution to the system of equations is \(x = 7\) and \(y=-4\)