Is (−2, 6)

Question

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

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 .

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

No, because the graphs don’t intersect at (−2, 6)
.

Answer 1

To determine if \((-2, 6)\) is a solution to the system of equations given by

1. \(x + 2y = 10\)
2. \(3x + y = 0\),

we need to substitute \(x = -2\) and \(y = 6\) into both equations and check if they hold true.

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

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

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

Thus, the correct response is:

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