To determine whether the point \((-4, 4)\) is a solution to the given system of equations, we need to substitute \(x = -4\) and \(y = 4\) into each equation and check if both equations hold true.
The system of equations is:
- \(y = -\frac{1}{4}x + 3\)
- \(y = x + 9\)
Check the first equation:
Substituting \(x = -4\) into the first equation: \[ y = -\frac{1}{4}(-4) + 3 \] \[ y = 1 + 3 \] \[ y = 4 \]
This matches the \(y\)-value provided, so \((-4, 4)\) satisfies the first equation.
Check the second equation:
Substituting \(x = -4\) into the second equation: \[ y = -4 + 9 \] \[ y = 5 \]
This does not match the \(y\)-value provided (which is \(4\)). Thus, \((-4, 4)\) does not satisfy the second equation.
Conclusion: The point \((-4, 4)\) is not a solution to the system of equations because it does not satisfy both equations.