Is (−2, 6)

Question

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

Answer 1

To determine if the point \((-2, 6)\) is a solution to the system of equations, we need to substitute \(x = -2\) and \(y = 6\) into both equations and see if they hold true.

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

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

Since the point \((-2, 6)\) satisfies both equations, we conclude that \((-2, 6)\) is indeed a solution to the system of equations.