Question 363982
{{{x-y+z=6}}}
{{{x+y+z=2}}}
{{{x+y-z=0}}}

Subtract 2nd equation from the 1st one:
{{{ -2y = 4 }}}
{{{ y = -2 }}}

Subtract 3rd equation from 2nd one:
{{{ 2z = 2  }}}
{{{ z = 1 }}}

Use 3rd equation fo find x:
{{{x = z - y}}}
{{{x = 3}}}