To solve the system of equations given by:
- \(-5x - 9y = 33\)
- \(-y - 1 = x\)
Let's first rewrite the second equation to express \(y\) in terms of \(x\):
\[ -y - 1 = x \implies -y = x + 1 \implies y = -x - 1 \]
Now we can substitute \(y\) in the first equation with \(-x - 1\):
\[ -5x - 9(-x - 1) = 33 \]
Distributing the \(-9\):
\[ -5x + 9x + 9 = 33 \]
Combining like terms:
\[ 4x + 9 = 33 \]
Subtracting \(9\) from both sides:
\[ 4x = 24 \]
Dividing by \(4\):
\[ x = 6 \]
Now that we have \(x\), we can find \(y\) using the equation \(y = -x - 1\):
\[ y = -6 - 1 = -7 \]
Thus, the solution to the system of equations is:
\[ x = 6, \quad y = -7 \]
So the solution is \((6, -7)\).