Question

What is the solution to the system of equations below?

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

(-8,2)
(-8,-1)
(8,-10)
(8,10)​

Answer 1

(- 8, 2 )

Explanation:

y =
`(1)/(2)` x + 6 → (1)

y = -
`(3)/(4)` x - 4 → (2)

substitute y =
`(1)/(2)` x + 6 into (2)

`(1)/(2)` x + 6 = -
`(3)/(4)`x - 4

multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions

2x + 24 = - 3x - 16 ( add 3x to both sides )

5x + 24 = - 16 ( subtract 24 from both sides )

5x = - 40 ( divide both sides by 5 )

x = - 8

substitute x = - 8 into either of the 2 equations and evaluate for y

substituting into (1)

y =
`(1)/(2)` (- 8) + 6 = - 4 + 6 = 2

solution is (- 8, 2 )