Question 1134190

 {{{x+2y-z=3}}}.....eq.1
{{{2x-y+z=22}}}....eq.2
{{{x+3y-z=4 }}}.....eq.3

start with

 {{{x+2y-z=3}}}.....eq.1
{{{x+3y-z=4 }}}.....eq.3
---------------------------------subtract
 {{{x+2y-z-(x+3y-z)=3-4}}}
 {{{x+2y-z-x-3y+z=-1}}}
 {{{cross(x)+2y-cross(z)-cross(x)-3y+cross(z)=-1}}}
{{{2y-3y=-1}}}
{{{-y=-1}}}
{{{highlight(y=1)}}}

{{{2x-y+z=22}}}....eq.2.... plug in {{{y=1}}}
{{{2x-1+z=22}}}
{{{2x+z=23}}}........solve for {{{z}}}
{{{z=-2x+23}}}........eq.2a

{{{x+3y-z=4 }}}.....eq.3...plug in {{{y=1}}}
{{{x+3*1-z=4 }}}
{{{x+3-z=4 }}}.....solve for {{{z}}}
{{{x+3-4=z }}}
{{{z=x-1 }}}....eq.3a

from eq.2a and eq.3a we have

{{{x-1=-2x+23}}}
{{{x+2x=23+1}}}
{{{3x=24}}}
{{{highlight(x=8)}}}

go to {{{z=x-1 }}}....eq.3a plug in {{{x}}} value

{{{z=8-1 }}}
{{{highlight(z=7) }}}

solutions: {{{highlight(8)}}},{{{highlight(1)}}},{{{highlight(7) }}}