The solution set x= (b1c2−b2c1)(a1b2−a2b1) and y= (c1a2−c2a1)(a1b2−a2b1) to the pair of linear equations given below can be written as:
a1x + b1y + c1=0 and a2x + b2y + c2=0 .
x/b1c2−b2c1 = y/a2c1−a1c2 = 1/b2a1−b1a2
We have x = b1c2−b2c1(a1b2−a2b1 and y = c1a2−c2a1a1b2−a2b1
We can write this as xb1c2−b2c1 = ya2c1−a1c2 = 1b2a1−b1a2
This is the basis for cross multiplication method.