Is (7, 3) the solution to the system of these linear equations: 3x+2y=5 and −x+6y=11 ? Why?(1 point) Responses 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 . 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 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) .

Question

GPT-4o mini · Answer

To determine if (7, 3) is a solution to the system of equations 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.

For the first equation 3x + 2y = 5: \[ 3(7) + 2(3) = 21 + 6 = 27 \neq 5 \] This shows that (7, 3) does not satisfy the first equation.
For the second equation -x + 6y = 11: \[ -(7) + 6(3) = -7 + 18 = 11 \] This shows that (7, 3) does satisfy the second equation.

Since (7, 3) does not satisfy the first equation, it is not a solution to the system of equations as both equations must be satisfied by the same pair of (x, y) values.

Therefore, the correct response is: No, because the graphs intersect at (7, 3).