It's Diophantine equation.
First, we need to found gcd(6,(-2)):
6=23
(-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.
\(\frac{24}{2} =12\)
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.
