To solve the system of equations using substitution, we start with the two equations:
- \(-y = x\)
- \(9x - 7y = -16\)
First, we will solve the first equation for \(y\): \[ y = -x \]
Next, we substitute this expression for \(y\) in the second equation: \[ 9x - 7(-x) = -16 \]
This simplifies to: \[ 9x + 7x = -16 \]
Combining like terms gives: \[ 16x = -16 \]
Now, we solve for \(x\): \[ x = \frac{-16}{16} = -1 \]
With \(x = -1\), we now substitute this value back into the equation \(y = -x\) to find \(y\): \[ y = -(-1) = 1 \]
Thus, the solution to the system of equations is: \[ (x, y) = (-1, 1) \]
The solution is: \[ \boxed{(-1, 1)} \]