To determine if the point (5, -1) is a solution to the system of linear equations given by \(x + y = 4\) and \(2x + 3y = 7\), we can substitute \(x = 5\) and \(y = -1\) into both equations and check if they hold true.
- For the first equation \(x + y = 4\):
\[ 5 + (-1) = 4 \ 4 = 4 \quad \text{(True)} \]
- 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 when we plug in \(x = 5\) and \(y = -1\), the point (5, -1) is indeed a solution to the system of equations.
So the correct response is:
Yes, because the graphs intersect at (5,−1).