Question

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)

Answer 1

A: (–8, 2)

Explanation:

Answer 2

A. (–8, 2)

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