Question

Is (5,−1) a solution to the system of these linear equations: x+y=4 and 2x+3y=7 ? Why?

Yes, because the graphs intersect at (5,−1).

No, because the graphs intersect at (5,−1).

No, because the graphs don’t intersect at (5,−1).

Yes, because the graphs don’t intersect at (5,−1).

Answer 1

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.

1. For the first equation, \( x + y = 4 \):
- Substitute: \( 5 + (-1) = 4 \)
- Calculation: \( 5 - 1 = 4 \)
- This is true.

2. 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).**