To determine if the point \((-4, 5)\) is a solution to the system of equations given by:
- \( x = -4 \)
- \( y = \frac{1}{2}x + 7 \)
we can substitute \(x = -4\) and \(y = 5\) into the second equation and check if it holds true.
First, let's substitute \(x = -4\) into the second equation:
\[ y = \frac{1}{2}(-4) + 7 \]
Calculating this:
\[ y = -2 + 7 \] \[ y = 5 \]
Now, we see that when \(x = -4\), \(y\) does indeed equal \(5\). Therefore, the point \((-4, 5)\) satisfies both equations.
Thus, \((-4, 5)\) is a solution to the system of equations.