To determine if \((-5, -8)\) is a solution to the system of equations given by
- \(y = 3x + 7\)
- \(y = 2x + 2\)
we will substitute \(x = -5\) and \(y = -8\) into both equations and see if the equations hold true.
For the first equation: \[ y = 3x + 7 \] Substituting \(x = -5\): \[ y = 3(-5) + 7 \ y = -15 + 7 \ y = -8 \] This holds true since \(-8 = -8\).
For the second equation: \[ y = 2x + 2 \] Substituting \(x = -5\): \[ y = 2(-5) + 2 \ y = -10 + 2 \ y = -8 \] This also holds true since \(-8 = -8\).
Since both equations are satisfied by the point \((-5, -8)\), we can conclude that \((-5, -8)\) is indeed a solution to the system of equations.