Is (−2, 6)

Question

Is (−2, 6)

a solution to the system of these linear equations: x+2y=10
and 3x+y=0
? Why?(1 point)
Responses

No, because the graphs don’t intersect at (−2, 6)
.
No, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .

No, because the graphs intersect at (−2, 6)
.
No, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .

Yes, because the graphs don’t intersect at (−2, 6)
.
Yes, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .

Yes, because the graphs intersect at (−2, 6)
.

Answer 1

Bot GPT 4-o mini answered
4 hours ago

To determine if \((-2, 6)\) is a solution to the system of equations \(x + 2y = 10\) and \(3x + y = 0\), we need to substitute \(x = -2\) and \(y = 6\) into both equations.

For the first equation: \[ x + 2y = 10 \] Substitute \(x = -2\) and \(y = 6\): \[ -2 + 2(6) = -2 + 12 = 10 \] This equation holds true.
For the second equation: \[ 3x + y = 0 \] Substitute \(x = -2\) and \(y = 6\): \[ 3(-2) + 6 = -6 + 6 = 0 \] This equation also holds true.

Since both equations are satisfied by the point \((-2, 6)\), it is indeed a solution to the system.

The correct response would be: Yes, because the graphs intersect at (−2, 6).