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

Question

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

B. No, because the graphs don’t intersect at (−2, 6).

C. Yes, because the graphs don’t intersect at (−2, 6).

D. Yes, because the graphs intersect at (−2, 6).

Answer 1

B. No, because the graphs don’t intersect at (−2, 6).

To check if (-2, 6) is a solution to the system of equations, we substitute x = -2 and y = 6 into both equations:

1. x + 2y = 10
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10 (true)

2. 3x + y = 0
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0 (true)

Since both equations are true when x = -2 and y = 6, (-2, 6) is indeed a solution to the system of linear equations.