What is the solution to the system of equations below?

y=1/2x+6 and y=3/4x-4

A. (-8, 2)

B. (-8, - 1)

C. (8, 10)

D. (8, - 10)

A. (-8, 2)

Step-by-step explanation:

(1) y = ½x + 6

(2) y = - ¾x - 4 Set (1) = (2)

½x + 6 = - ¾x - 4 Multiply each side by 4

2x + 24 = - 3x - 16 Add 16 to each side

2x + 40 = - 3x Subtract 2x from each side

40 = - 5x Divide each side by - 5

(3) x = - 8 Substitute (2) into (1)

y = ½ (-8) + 6

= - 4 + 6

= 2

The solution to the system of equations is (-8,2).

You can see the graphs of the two functions in the figure below. The two lines intersect at (-8, 2).

Check:

2 = ½ (-8) + 6 2 = - ¾ (-8) - 4

2 = - 4 + 6 2 = 6 - 4

2 = 2 2 = 2