# Solve the system of equations: 2/x + 3/y + 10/z = 4 4/x - 6/y + 5/z = 1

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Solve the system of equations:

2/x + 3/y + 10/z = 4

4/x - 6/y + 5/z = 1

6/x + 9/y - 20/z = 2

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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

Cofactors of A are

A11 = 120 − 45 = 75,

A12 = − ( − 80 − 30) = 110,

A13 = (36 + 36) = 72,

A21 = − ( − 60 − 90) = 150,

A22 = ( − 40 − 60) = − 100,

A23 = − (18 − 18) = 0,

A31 = 15 + 60 = 75,

A32 = − (10 − 40) = 30,

A33 = − 12 − 12 = − 24