The easiest method is to draw arrow diagram.
Let us take two equations:
a1x+b1y+c1=0
a2x+b2y+c2=0
Draw the arrow diagram as follows:
The first pair will be under x, second will be under y and third will be under constant number 1.
So the equation will be
xb1c2−b2c1=yc1a2−c2a1=1a1b2−a2b1