To determine if the point \((-4, -5)\) is a solution to the system of equations, we need to substitute \(x = -4\) and \(y = -5\) into both equations.
The equations are:
- \(y = -2x - 13\)
- \(y = -x + 1\)
For the first equation:
Substituting \(x = -4\) into \(y = -2x - 13\):
\[ y = -2(-4) - 13 \] \[ y = 8 - 13 \] \[ y = -5 \]
This matches \(y = -5\).
For the second equation:
Substituting \(x = -4\) into \(y = -x + 1\):
\[ y = -(-4) + 1 \] \[ y = 4 + 1 \] \[ y = 5 \]
This does not match \(y = -5\).
Since the point \((-4, -5)\) satisfies the first equation but not the second equation, it is not a solution to the system of equations.
Therefore, \((-4, -5)\) is not a solution to this system.