Question

is -2,6 a solution to the system of these linear equationd x+2y=10 and 3x+y=0 no because the graph dont intersect at -2,6 yes because the graphs dont intersect at -2,6 yes becasue the grpahs intersect at -2,6 no because the graphs intersect at -2,6

Answer 1

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

1. **First equation: \(x + 2y = 10\)**
Substitute \(x = -2\) and \(y = 6\):
\[
-2 + 2(6) = -2 + 12 = 10
\]
This equation is satisfied.

2. **Second equation: \(3x + y = 0\)**
Substitute \(x = -2\) and \(y = 6\):
\[
3(-2) + 6 = -6 + 6 = 0
\]
This equation is also satisfied.

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

The correct answer is:
**Yes, because the graphs intersect at \((-2, 6)\).**