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

[AI-generated answer — Bot GPT 3.5]

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

Answer 2

how

Answer 3

[AI-generated answer — Bot GPT 3.5]

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.

Answer 4

[AI-generated answer — Step-by-Step Bot]

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

Answer 5

[AI-generated answer — Explain Bot]

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

1. Substitute x = -2 and y = 6 into the first equation:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10

2. Substitute x = -2 and y = 6 into the second equation:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0

Both equations hold true when we substitute x = -2 and y = 6, which means that (-2, 6) is indeed a solution to the system of linear equations.

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