Ax + by = 1, bx + ay = 0
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Multiply equation 1 by b and equation 2 by a,you will get
abx+b square y=b----3
abx+a square y=0 ---4
equation 3 minus equation 4
abx+b square y - (abx+a square y) = b
abx+b square y - abx -a square y=b
b square y - a square y=b
y(b square - a square )=b
y= b/b2-a2,substitute this value in either equation 1 or 2,you will get x= -a/b2-a2
abx+b square y=b----3
abx+a square y=0 ---4
equation 3 minus equation 4
abx+b square y - (abx+a square y) = b
abx+b square y - abx -a square y=b
b square y - a square y=b
y(b square - a square )=b
y= b/b2-a2,substitute this value in either equation 1 or 2,you will get x= -a/b2-a2
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