To solve the system of equations:
- Equation 1: \(-9x - y = 9\)
- Equation 2: \(x + 2y = 16\)
We can use the substitution or elimination method. Here, I'll use the substitution method.
First, let's solve Equation 1 for \(y\):
\[ -y = 9 + 9x \] \[ y = -9x - 9 \]
Now, substitute this expression for \(y\) into Equation 2:
\[ x + 2(-9x - 9) = 16 \] \[ x - 18x - 18 = 16 \] \[ -17x - 18 = 16 \] \[ -17x = 16 + 18 \] \[ -17x = 34 \] \[ x = -2 \]
Now that we have the value of \(x\), we can substitute it back into the expression we found for \(y\):
\[ y = -9(-2) - 9 \] \[ y = 18 - 9 \] \[ y = 9 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-2, 9) \]
So the answer is \((-2, 9)\).