Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0? Why?(1 point)
Responses
No, because the graphs intersect at (−2, 6).
No, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .
No, because the graphs don’t intersect at (−2, 6).
No, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .
Yes, because the graphs don’t intersect at (−2, 6).
Yes, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .
Yes, because the graphs intersect at (−2, 6).
No, because the graphs intersect at (-2, 6).
No, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .
No, because the graphs don’t intersect at (−2, 6).
To determine if the point (-2, 6) is a solution to the system of equations x + 2y = 10 and 3x + y = 0, we can substitute the values of x and y into each equation and see if the equations are satisfied.
1. Substitute x = -2 and y = 6 into the first equation, x + 2y = 10:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
2. Substitute x = -2 and y = 6 into the second equation, 3x + y = 0:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Both equations are satisfied when we substitute the values of x = -2 and y = 6. Therefore, (-2, 6) is a solution to the system of linear equations.
So, the correct response is:
Yes, because the graphs don’t intersect at (-2, 6).