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 don’t intersect at (−2, 6)

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

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

Answer 1

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

1. For the first equation: \[ x + 2y = 10 \ -2 + 2(6) = 10 \ -2 + 12 = 10 \ 10 = 10 \quad \text{(True)} \]

2. For the second equation: \[ 3x + y = 0 \ 3(-2) + 6 = 0 \ -6 + 6 = 0 \ 0 = 0 \quad \text{(True)} \]

Since both equations are satisfied, (−2, 6) is indeed a solution to the system.

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