Question

Is (−2, 6)
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.