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

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step-by-step explanation:

yes.. it's proven to be 36.