Here x and y have the same coefficient a1b2 - a2b1. This is called a determinant of the second order, and is written
|a1, b1|
|a2, b2|.
We may now write
| x | a1, b1 a2, b2 | = | c1, b1 c2, b2 | . |
Similarly with three equations,
a1x + b1y + c1z = d1,
a2x + b2y + c2z = d2,
a3x + b3y + c3z = d3,
we find