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

Question

A. no, because the graphs intersect at (-2, 6)
B. no because the graphs dont intersect at (-2, 6)
C. yes, because the graphs intersect at (-2, 6)
D. yes because the graphs dont intersect at (-2, 6)

Answer 1

To determine if (-2, 6) is a solution to the system of linear equations, we substitute the values of x and y into the equations and check if they are satisfied.

For the first equation, x + 2y = 10:
(-2) + 2(6) = 10
-2 + 12 = 10
10 = 10

For the second equation, 3x + y = 0:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0

Both equations are satisfied when x = -2 and y = 6. Therefore, (-2, 6) is a solution to the system of linear equations.

The correct answer is: C. yes, because the graphs intersect at (-2, 6)