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 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 equations \(x + 2y = 10\) and \(3x + y = 0\), we need to substitute \(x = -2\) and \(y = 6\) into both equations.

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

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

Since (−2, 6) satisfies both equations, it is indeed a solution to the system. Therefore, the correct response is:

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