Is (7, 3)

Question

the solution to the system of these linear equations: 3x+2y=5
and −x+6y=11
? Why?(1 point)
Responses

Yes, because the graphs don’t intersect at (7, 3)
.
Yes, because the graphs don’t intersect at left parenthesis 7 comma 3 right parenthesis .

No, because the graphs don’t intersect at (7, 3)
.
No, because the graphs don’t intersect at left parenthesis 7 comma 3 right parenthesis .

No, because the graphs intersect at (7, 3)
.
No, because the graphs intersect at left parenthesis 7 comma 3 right parenthesis .

Yes, because the graphs intersect at (7, 3)
.

Answer 1

To determine if (7, 3) is a solution to the system of equations, we need to substitute x = 7 and y = 3 into both equations.

1. For the first equation, \(3x + 2y = 5\): \[ 3(7) + 2(3) = 21 + 6 = 27 \] Since 27 does not equal 5, the point (7, 3) is not a solution for the first equation.

2. For the second equation, \(-x + 6y = 11\): \[ -7 + 6(3) = -7 + 18 = 11 \] Here, the point (7, 3) satisfies the second equation.

Since (7, 3) does not satisfy both equations, it is not a solution to the system.

Therefore, the correct response is:

No, because the graphs don’t intersect at (7, 3).