Question

How do you solve the system `7x + 2y = 2` and `6x - 2y = 8`?

Answer 1

I notice that all the terms in the second equation are divisible by 2 and it will be easy to isolate `y`, so let's do that first.

`6x-2y=8`

Divide both sides by 2 to get

`3x-y=4`

Add `y` to both sides to get

`3x=4+y`

Subtract 8 from both sides to get

`y = 3x-4`

Now substitute this expression for `y` into the first equation...

`2 = 7x+2y`

`= 7x + 2(3x-4)`

`= 7x + 6x - 8`

`=13x - 8`

Add 8 to both sides to get

`13x=10`

Divide both sides by 13 to get

`x = 10/13`

`y = 3x-4 = (3xx10)/13-4`

`= 30/13-(4xx13)/13`

`= (30-52)/13`

`= -22/13`