Question

1. 10x + 2y = -24

-x - y = 8

Explanation:

Step1: Simplify the second equation

From \(-x - y = 8\), we can multiply both sides by \(2\) to get \(-2x - 2y = 16\).

Step2: Add the two equations

Add \(10x + 2y = -24\) and \(-2x - 2y = 16\) together.
\((10x + 2y)+(-2x - 2y)=-24 + 16\)
Simplify the left side: \(10x - 2x+2y - 2y = 8x\)
Simplify the right side: \(-8\)
So we have \(8x=-8\)

Step3: Solve for \(x\)

Divide both sides of \(8x = -8\) by \(8\): \(x=\frac{-8}{8}=-1\)

Step4: Substitute \(x\) into the second equation to solve for \(y\)

Substitute \(x = -1\) into \(-x - y = 8\): \(-(-1)-y = 8\)
Simplify: \(1 - y = 8\)
Subtract \(1\) from both sides: \(-y = 8 - 1 = 7\)
Multiply both sides by \(-1\): \(y=-7\)

Answer:

The solution to the system of equations is \(x = -1\) and \(y = -7\)