Question

is -2,6 a solution to the system of these linear equationd x+2y=10 and 3x+y=0

Answer 1

To determine if \((-2, 6)\) is a solution to the system of equations \(x + 2y = 10\) and \(3x + y = 0\), we will substitute \(x = -2\) and \(y = 6\) into both equations and see if they hold true.

1. **Substituting into the first equation**:
\[
x + 2y = 10
\]
\[
-2 + 2(6) = 10
\]
\[
-2 + 12 = 10
\]
\[
10 = 10 \quad \text{(True)}
\]

2. **Substituting into the second equation**:
\[
3x + y = 0
\]
\[
3(-2) + 6 = 0
\]
\[
-6 + 6 = 0
\]
\[
0 = 0 \quad \text{(True)}
\]

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