Bezout's Identity to solve ax+by=1 (a,b) are coprime

This is the first tutorial of a sequence of Bézout's Identity to find the answer to ax+by=gcd(a,b) .
In this video we have 197x+51y=1 .
We are looking to solve the equation for x and y in the shortest possible way.
In this example the values of a,b are coprime , hence why we solve for x,y when the equation ax+by=1.
first we use Euclids Algorithm to find the gcd( greatest common divisor ) .
Then we go in a backwards direction starting from the end , rewriting the algorithm to make the remainder the subject of the equation .
At each stage we substitute the remainder with the calculations that gave us the remainder.
proof of answer 85x51=4335 , 22x197=4334
#euclidsalgorithm
#algebra
#algebra2inequalities
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