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 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

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

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

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

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

Thus, the correct response is:

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