Question

A system of equations is graphed on the coordinate plane. y=−2x−4 and y=2x+4. What is the solution to the system of equations? Enter the coordinates of the solution in the boxes ( , ​).

Answer 1

The solution to the system of equations y = -2x - 4 and y = 2x + 4 is found by setting them equal to each other, solving for x, and then finding the corresponding y value. The solution is (-2, 0).

Step-by-step explanation:

The student is asking about finding the solution to a system of linear equations that is graphed on a coordinate plane. The given equations are y = -2x - 4 and y = 2x + 4. To find the solution, we need to identify the point at which these two lines intersect, which is where their x and y values are equal.

Since both equations are set equal to y, we can set them equal to each other to find the x-coordinate of the intersection point:

-2x - 4 = 2x + 4

Solving for x, we combine like terms:

-2x - 2x = 4 + 4

-4x = 8

x = -2

Now we can substitute x = -2 into one of the original equations to find the corresponding y-coordinate:

y = 2(-2) + 4

y = -4 + 4

y = 0

Therefore, the coordinates of the solution to the system of equations are (-2, 0).