Question

How do you solve the following system?: `1/3y = 3/4x + 5 , 3/2x - 8y = 2`

Answer 1

`x=-244/33` `y=-18/11`

Explanation:

`(1/3)y=(3/4)x+5`----(1)
`(3/2)x-8y=2`----(2)

Multiply (2) by `(1/2)`
`(3/4)x-4y=1`----(3)

Add(1)and(3), to make`x`disappear
`(1/3)y+(3/4)x-4y=(3/4)x+5+1`
`(3/4)x-(3/4)x+(1/3)y-4y=5+1`
`(-11/3)y=6`
`y=6*(-3/11)`
`y=-18/11`

Substitude`y=-18/11`into(3)
`(3/4)x-4(-18/11)=1`
`(3/4)x+72/11=1`
`(3/4)x=1-72/11`
`(3/4)x=-(61/11)`
`x=-(61/11)*(4/3)`
`x=-244/33`

So, `x=-244/33` `y=-18/11`