To determine if the point \((-6, 4)\) is a solution to the system of equations:
- \(y = -3x - 14\)
- \(y = x + 10\)
we need to substitute \(x = -6\) and \(y = 4\) into both equations.
For the first equation: \[ y = -3x - 14 \]
Substituting \((-6, 4)\): \[ 4 = -3(-6) - 14 \] \[ 4 = 18 - 14 \] \[ 4 = 4 \quad \text{(True)} \]
For the second equation: \[ y = x + 10 \]
Substituting \((-6, 4)\): \[ 4 = -6 + 10 \] \[ 4 = 4 \quad \text{(True)} \]
Since the point \((-6, 4)\) satisfies both equations, it is indeed a solution to the system of equations.