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

Question

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).

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 .

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

Answer 1

To determine if the point \((-2, 6)\) 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 and check if they hold true.

1. Checking the first equation \(x + 2y = 10\):

   \[ -2 + 2(6) = -2 + 12 = 10 \]

   The first equation is satisfied.

2. Checking the second equation \(3x + y = 0\):

   \[ 3(-2) + 6 = -6 + 6 = 0 \]

   The second equation is also satisfied.

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

The correct answer is:

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