To determine if the point \((4, 10)\) is a solution to the system of equations, we need to check if it satisfies both equations:
- \( y = 2x + 2 \)
- \( y = 10x + 1 \)
First equation: Substitute \(x = 4\) and \(y = 10\) into the first equation:
\[ 10 = 2(4) + 2 \] \[ 10 = 8 + 2 \] \[ 10 = 10 \]
This equation is satisfied.
Second equation: Now substitute \(x = 4\) and \(y = 10\) into the second equation:
\[ 10 = 10(4) + 1 \] \[ 10 = 40 + 1 \] \[ 10 = 41 \]
This equation is not satisfied.
Since \((4, 10)\) satisfies the first equation but not the second one, we conclude that \((4, 10)\) is not a solution to the system of equations.