Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why?(1 point)

Question

Responses

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 .

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 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 can substitute \( x = -2 \) and \( y = 6 \) into each equation to see if the equations hold true.

For the first equation: \[ -2 + 2(6) = 10 \] \[ -2 + 12 = 10 \] \[ 10 = 10 \quad (True) \]

For the second equation: \[ 3(-2) + 6 = 0 \] \[ -6 + 6 = 0 \] \[ 0 = 0 \quad (True) \]

Since both equations hold true when substituting \( x = -2 \) and \( y = 6 \), we can conclude that (−2, 6) is indeed a solution to the system of equations.

Thus, the correct response is:

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