Question

Question

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

Yes, because the graphs intersect at (7, 3)
.
Yes, because the graphs intersect at (7, 3)
. - no response given

Yes, because the graphs don’t intersect at (7, 3)
.
Yes, because the graphs don’t intersect at (7, 3)
. - no response given

No, because the graphs don’t intersect at (7, 3)
.
No, because the graphs don’t intersect at (7, 3)
. - no response given

No, because the graphs intersect at (7, 3)
.

Answer 1

To determine if (7, 3) is the solution to the system of linear equations given by:

1. \( 3x + 2y = 5 \)
2. \( -x + 6y = 11 \)

we can substitute \( x = 7 \) and \( y = 3 \) into both equations and check if they are satisfied.

For the first equation:

\[ 3(7) + 2(3) = 5 \] \[ 21 + 6 = 5 \] \[ 27 \neq 5 \] So (7, 3) does not satisfy the first equation.

For the second equation:

\[ -7 + 6(3) = 11 \] \[ -7 + 18 = 11 \] \[ 11 = 11 \] So (7, 3) satisfies the second equation but not the first.

Conclusion:

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

The correct response is: No, because the graphs don’t intersect at (7, 3).