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 .

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 intersect at (7, 3)
.
No, 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 a solution to the system of equations given by \( 3x + 2y = 5 \) and \( -x + 6y = 11 \), we need to substitute \( x = 7 \) and \( y = 3 \) into both equations and check if they hold true.

1. Substituting into the first equation: \[ 3(7) + 2(3) = 21 + 6 = 27 \quad \text{(not equal to 5)} \]

2. Substituting into the second equation: \[ -7 + 6(3) = -7 + 18 = 11 \quad \text{(equal to 11)} \]

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

Thus, the correct response is:

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