a1x + b1y + c1z = d1

a2x + b2y + c2z = d2

a3x + b3y + c3z = d3

For example：

x1+x2-2x3=-3

2x1+x2-x3=1

x1-x2+3x3=8

Solve:

D =

1  1 -2

2  1 -1

1 -1  3

= 1

D1 =

-3  1 -2

1  1 -1

8 -1  3

= 1

D2 =

1 -3 -2

2  1 -1

1  8  3

= 2

D3 =

1  1 -3

2  1  1

1 -1  8

= 3

So x1 = D1/D = 1

 x2 = D2/D = 2

 x3 = D3/D = 3

 

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