Question

Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why? (1 point)

Answer 1

Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3

Answer 2

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

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

Since the equation is true, (-2, 6) satisfies the first equation.

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

Since the equation is true, (-2, 6) also satisfies the second equation.

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

Answer 3

To estimate the solution to the system of linear equations based on the graph, we need to see where the two lines intersect. By looking at the graph, we can estimate that the point of intersection is approximately (2, 20)