If we have \(2x+3y=1\), well by trial and error we can quickly see that \(x\) is \(2\) while \(y\) is \(-1\). But when we are given huge numbers it can be a bit more difficult. In order to work the equation out with nigger numbers the Euclidean algorithm must be applied. Let’s recall that Euclid’s theorem states: For any numbers and \(a,b,\) \(x,\) gcd \(\left(a,b\right)\)= gcd\(\left(b,a-bx\right)\).