Let 1/x = p, 1/y = q and 1/z = r, then the given equations become

2p + 3q + 10r = 4, 4p − 6q + 5r = 1, 6p + 9q − 20r = 2

This system can be written as AX = B, where

Thus, A is non-singular. Therefore, its inverse exists. Therefore, the above system is consistent and has a unique solution given by X = A ^{−1}B

Cofactors of A are

A_{11} = 120 − 45 = 75,

A_{12} = − ( − 80 − 30) = 110,

A_{13} = (36 + 36) = 72,

A_{21} = − ( − 60 − 90) = 150,

A_{22} = ( − 40 − 60) = − 100,

A_{23} = − (18 − 18) = 0,

A_{31} = 15 + 60 = 75,

A_{32} = − (10 − 40) = 30,

A_{33} = − 12 − 12 = − 24