Question

How do you solve the following system: #2x - 3y = 10 , 2x + 3y = 12#?

Answer 1

`color(white)(xx)x=11/2`, and `y=1/3`

Explanation:

`color(white)(xx)2x-3y=10,color(white)(x)2x+3y=12`

`color(white)(xx)2x-3y=10<=>3y=2x-10`
`color(white)(xx)2x+3y=12<=>3y=-2x+12`

`=>2x-10=y`
`=>2x-10=color(red)(-2x+12)`

Add `color(red)(+2x+10)` to both side:
`color(white)(xx)2x-10color(red)(+2x+10)=-2x+12color(red)(+2x+10)`
`=>4x=22`

Multiply both sides by `color(red)(1/4)`:
`color(white)(xx)color(red)(1/4xx)4x=color(red)(1/4xx)22`
`=>x=11/2`

`color(white)(xx)3y=2x-10`
`=>3y=2xxcolor(red)(11/2)-10`
`=>3y=1`

`=>color(red)(1/3xx)3y=color(red)(1/3xx)1`
`=>y=1/3`