To determine if the point \( (5, -1) \) is a solution to the system of equations given by:
- \( x + y = 4 \)
- \( 2x + 3y = 7 \)
we can substitute \( x = 5 \) and \( y = -1 \) into both equations and check if they hold true.
For the first equation:
\[ x + y = 4 \ 5 + (-1) = 4 \ 5 - 1 = 4 \ 4 = 4 \quad \text{(True)} \]
For the second equation:
\[ 2x + 3y = 7 \ 2(5) + 3(-1) = 7 \ 10 - 3 = 7 \ 7 = 7 \quad \text{(True)} \]
Since both equations are satisfied by the point \( (5, -1) \), we conclude that \( (5, -1) \) is indeed a solution to the system of equations.