Question

6x-2y=24
how do u solve for y

Answer 1

6x - 2y = 24

-2y = 24 - 6x Multiply both sides by -1

2y = 6x - 24 Divide both sides by 2

y = (6x - 24)/2

y = 6x/2 - 24/2

y = 3x - 12

Answer 2

It's Diophantine equation.
First, we need to found gcd(6,(-2)):
6=2*3
(-2)=(-1)*2

So, gcd(6,-2)=2
Now, the question is. Can we dived c=24, by gcd(6,-2) and in the end get integer?
Yes we can.

`(24)/(2) =12`
So, we can solve it.

Now is the formula:

`{\displaystyle {\begin{cases}x=x_(0)+n{\frac {b}{\gcd(a,\;b)}}\\y=y_(0)-n{\frac {a}{\gcd(a,\;b)}}\end{cases}}\quad n\in \mathbb {Z} .}`

Second, we need the first pair (x0,y0)
if
x=0
then

`y=(-12)`

Third, we gonna use that formula:

`{\displaystyle {\begin{cases}x=-n}\\y=-3(4+n)}\end{case}\quad n\in \mathbb {Z} .}`
Congratulations! We solve it.