Question

Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why?(1 point)ResponsesNo, because the graphs intersect at (−2, 6).No, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .Yes, because the graphs intersect at (−2, 6).Yes, 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 .

Answer 1

how

Answer 2

No, because the point (-2, 6) is not a solution to the system of equations.

Answer 3

To determine if a point is a solution to a system of linear equations, we substitute the values of the point into each equation and check if the equations are true.

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

So the point (-2, 6) satisfies the first equation.

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

So the point (-2, 6) satisfies the second equation as well.

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