Question 113455
There are 3 equations with 3 unknowns, so it should be possible
to find x, y, and z.
{{{ x + 5y - z = 4}}}
{{{3x + 4y + z = 4}}}
{{{ x - y + z = 0}}}
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add the 1st and 3rd
{{{ x + 5y - z =4}}}
{{{ x- y + z =0}}}
{{{2x + 4y = 4}}}
{{{4y = 4 - 2x}}}
{{{y = 1 - (1/2)x}}}
subtract this equation from the 2nd one
{{{3x + 4y + z =4}}}
{{{2x + 4y = 4}}}
{{{x + z = 0}}}
{{{z = -x}}}
Now plug values for y and z into the 3rd equation
{{{ x - y + z = 0}}}
{{{x - (1 - (1/2)x) + (-x) = 0}}}
{{{x - 1 + (1/2)x - x = 0}}}
{{{(1/2)x = 1}}}
{{{x = 2}}}
{{{z = -2}}}
{{{y = 1 - (1/2)*2}}}
{{{y = 0}}}
The answers are 
x = 2
y = 0
z = -2
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check answers
{{{ x + 5y - z = 4}}}
{{{3x + 4y + z = 4}}}
{{{ x - y + z = 0}}}
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{{{2 + 5*0 - (-2) = 4}}}
{{{2 + 2 = 4}}}
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{{{3*2 + 4*0 + (-2) = 4}}}
{{{6 - 2 = 4}}}
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{{{2 - 0 + (-2) = 0}}}
{{{2 - 2 = 0}}}
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OK