Question

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

Yes, because the graphs intersect at (5,−1)
.
Yes, because the graphs intersect at left parenthesis 5 comma negative 1 right parenthesis .

No, because the graphs don’t intersect at (5,−1)
.
No, because the graphs don’t intersect at left parenthesis 5 comma negative 1 right parenthesis .

No, because the graphs intersect at (5,−1)
.
No, because the graphs intersect at left parenthesis 5 comma negative 1 right parenthesis .

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

Answer 1

To determine whether (5, -1) is a solution to the given system of equations, we should substitute x = 5 and y = -1 into both equations:

1. For the first equation \( x + y = 4 \):
\[
5 + (-1) = 4 \\
4 = 4 \quad \text{(True)}
\]

2. For the second equation \( 2x + 3y = 7 \):
\[
2(5) + 3(-1) = 7 \\
10 - 3 = 7 \\
7 = 7 \quad \text{(True)}
\]

Since (5, -1) satisfies both equations, it is indeed a solution to the system.

The correct response is:
**Yes, because the graphs intersect at (5,−1).**