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 each equation and check if the equations hold true.
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For the first equation, \( x + y = 4 \):
- Substitute: \( 5 + (-1) = 4 \)
- Calculation: \( 5 - 1 = 4 \)
- This is true.
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For the second equation, \( 2x + 3y = 7 \):
- Substitute: \( 2(5) + 3(-1) = 7 \)
- Calculation: \( 10 - 3 = 7 \)
- This is also true.
Since (5, −1) satisfies both equations, it is indeed a solution to the system.
Therefore, the correct answer is: Yes, because the graphs intersect at (5,−1).