Question

A system of equations is graphed on the coordinate plane.

y=-3x-9
y=3x+9
What is the solution to the system of equations?
A. (0,3)
B. (-3.0) C. (3.0)
D. (0,-3)

Answer 1

The solution to the system of equations y = -3x - 9 and y = 3x + 9 is found by setting the two equations equal to each other and solving for x, then replacing x in either equation to find y. The solution is the point (-3,0), which is option B.

Step-by-step explanation:

The system of equations is y = -3x - 9 and y = 3x + 9. To find the solution to the system of equations, set the two equations equal to each other since they both equal y:

-3x - 9 = 3x + 9

Combine like terms:

-3x - 3x = 9 + 9

-6x = 18

Divide both sides by -6 to solve for x:

x = -3

Substitute x = -3 into one of the original equations to solve for y:

y = 3(-3) + 9

y = -9 + 9

y = 0

The point (-3,0) is where the two lines intersect, making it the solution of the system. This corresponds to choice B.