Is (−2, 6)

Question

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

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

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 .

Yes, because the graphs intersect at (−2, 6)
.
Yes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .

Yes, because the graphs don’t intersect at (−2, 6)

Answer 1

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

1. For the first equation \( x + 2y = 10 \): \[ -2 + 2(6) = -2 + 12 = 10 \] This equation is satisfied.

2. For the second equation \( 3x + y = 0 \): \[ 3(-2) + 6 = -6 + 6 = 0 \] This equation is also satisfied.

Since (−2, 6) satisfies both equations, it is a solution to the system.

Therefore, the correct response is: Yes, because the graphs intersect at (−2, 6).