Question

1. -x - 7y = -29

9x + 6y = -24

Explanation:

Step1: Solve the first equation for \(x\)

From \(-x - 7y = -29\), we can rewrite it as:
\(-x = 7y - 29\)
Multiply both sides by \(-1\) to get:
\(x = -7y + 29\)

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

The second equation is \(9x + 6y = -24\). Substitute \(x = -7y + 29\) into it:
\(9(-7y + 29) + 6y = -24\)
Expand the left side:
\(-63y + 261 + 6y = -24\)
Combine like terms:
\(-57y + 261 = -24\)

Step3: Solve for \(y\)

Subtract 261 from both sides:
\(-57y = -24 - 261\)
\(-57y = -285\)
Divide both sides by \(-57\):
\(y = \frac{-285}{-57} = 5\)

Step4: Substitute \(y = 5\) back into \(x = -7y + 29\)

\(x = -7(5) + 29\)
\(x = -35 + 29\)
\(x = -6\)

Answer:

The solution to the system of equations is \(x = -6\) and \(y = 5\)