Solving Systems of Equations by Graphing Quick Check

Question

2 of 52 of 5 Items

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

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

No, because the graphs intersect at (−2, 6).

Answer 1

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

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

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

Since both equations are satisfied by the coordinates \((-2, 6)\), we conclude that \((-2, 6)\) is indeed a solution to the system of equations.

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