Question 127055
Try solving out system of equation with four variables. 
x + y + z + w =  0  
x + y - z - w =  1
x - y + z + w =  3
x - y - z + w = -1

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I used the Matrix function of a TI calculator to get the following:
x = 2
y = -3/2
z = 2
w = -5/2
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Cheers,
Stan H.