Question

How do you solve the following system: #2x-6y=-12 , 2x + y = 8 #?

Answer 1

`(x,y)=(18/7,20/7)`

Explanation:

Given:
[1]`color(white)("XXX")2x-6y=-12`
[2]`color(white)("XXX")2x+y=8`

Subtract equation [1] from equation [2] to get:
[3]`color(white)("XXX")7y=20`

Divide both sides of equation [3] by `7`:
[4]`color(white)("XXX")y=20/7`

Substitute `20/7`, the value given for `y` in equation [4], for `y` in equation [2]
[5]`color(white)("XXX")2x+20/7=8`

Subtract `20/7` from both sides of equation [5] and simplify the right side
[6]`color(white)("XXX")2x=8-20/7 = 56/7-20/7 = 36/7`

Divide both sides of equation [6] by `2`
`color(white)("XXX")x=18/7`