First number:  x

Second number: y

Third number:  z





The sum of the 1st number and 2 times the third: x + 2z

Then subtract the 2nd number x + 2z - y, or x - y + 2z to keep things in order.

The result is 1:  x - y + 2z = 1





2 times the 1st number: 2x

Plus the 3rd number:    2x + z

'is' means equals, so   2x + z = 3





The 1st number, x, plus 3 times the 2nd, 3y, plus the 3rd, z 

is (=) 18, so:

x + 3y + z = 18





So, here are your three equations.

 x -  y + 2z = 1

2x      +  z = 3

 x + 3y +  z = 18





Looking at the coefficients, I would say that Gauss-Jordan elimination is the

best solution method.  But you do it however you like. 

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