Question

How do you solve the following system?: `3x+3y=-21 , 6x+5y=18`

Answer 1

`x=53, \ \ y=-60`

Explanation:

Given equations

`3x+3y=-21\ ........(1)`

`6x+5y=18\ ........(2)`

Multiplying (1) by `2` & subtracting from (2) as follows

`6x+5y-2(3x+3y)=18-2(-21)`

`6x+5y-6x-6y=18+42`

`-y=60`

`y=-60`

Setting the value of `y` in (1), we get

`3x+3(-60)=-21`

`3x-180=-21`

`3x=180-21`

`x=\frac{159}{3}`

`x=53`

Answer 2

`x=53` and `y=-60`

Explanation:

`2*(3x+3y)-(6x+5y)=2*(-21)-18`

`(6x+6y)-(6x+5y)=(-42)-18`

`y=-60`

So,

`3x+3*(-60)=-21`

`3x-180=-21`

`3x=159` or `x=53`