Is (7, 3)

Question

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

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

Yes, because the graphs intersect at (7, 3)
.
Yes, because the graphs intersect at left parenthesis 7 comma 3 right parenthesis .

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

Answer 1

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

1. For the first equation: \[ 3x + 2y = 5 \] Substitute \(x = 7\) and \(y = 3\): \[ 3(7) + 2(3) = 21 + 6 = 27 \neq 5 \] So, (7, 3) does not satisfy the first equation.

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

Since (7, 3) does not satisfy the first equation, it is not a solution to the system of equations. The correct response is:

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