Question

What is the solution to the system of equations below?

y = one-half x + 6 and y = negative three-fourths x minus 4
(–8, 2)
(–8, –1)
(8, 10)
(8, –10)

Answer 1

(-8, 2)

Explanation:

1. Set up the equations.

y = 1/2x + 6

y = -3/4x - 4

2. Set the equations to equal each other.

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

3. Move the variables to one side and the numbers to the opposite side.

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

10 = -3/4x - 2/4x

10 = -5/4x

4. Divide 10 by -5/4.

10/ -5/4 = 10 * -4/5 (when dividing fractions, flip the fraction over)

10 * -4/5 = -40/5 = -8

x = -8

5. Plug in the x-value into one of the equations.

y = 1/2x + 6

y = 1/2(-8) + 6

y = -4 + 6

y = 2

OR

y = -3/4x - 4

y = -3/4(-8) - 4

y = 6 - 4

y = 2