Question 1131323
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x-y+5z=19
3x+z=4
x+2y+z=6
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E2 gives {{{z=4-3x}}}.


2*E1+E3 gives  {{{3x+11z=44}}}


Substitute for z in that result:
{{{3x+11(4-3x)=44}}}
-
{{{3x+44-33x=44}}}
{{{-3x=0}}}
{{{highlight(x=0)}}}
This is one of the variables solved.  


Returning to E2,
{{{3x+z=4}}}
{{{z=4-3x}}}
{{{z=4-3*0}}}
{{{highlight(z=4)}}}
Another variable now solved.


Use both of these values to find the last or y variable.