Question 1121369

{{{x-2y+3z=-11}}}.....(1)
{{{2x-z=8}}}.....(2)
{{{3y+z=10}}}.....(3)

start with (2) and (3)

 {{{2x-z=8}}}.....(2)
{{{3y+z=10}}}.....(3).............   add them
-------------------------------------------

{{{2x-z+3y+z=8+10}}}

{{{2x+3y=18}}}.........(a)

go with (1) and (3)

{{{x-2y+3z=-11}}}.....(1)
{{{3y+z=10}}}.....(3)............both sides multiply by {{{3}}}
--------------------------------------
{{{x-2y+3z=-11}}}.....(1)
{{{9y+3z=30}}}.....(3)
-------------------------------------------------.................subtract (3) from (1)

{{{x-2y+3z-(9y+3z)=-11-30}}}
{{{x-2y+3z-9y-3z=-41}}}

{{{x-11y=-41}}}...........(b)

go with (a) and (b)

{{{2x+3y=18}}}.........(a)
{{{x-11y=-41}}}...........(b).......both sides multiply by {{{2}}}
--------------------------------

{{{2x+3y=18}}}.........(a)
{{{2x-22y=-82}}}...........(b)
--------------------------------------------------subtract (b) from (a)

{{{2x+3y -(2x-22y)=18-(-82)}}}

{{{2x+3y -2x+22y=18+82}}}

{{{3y +22y=100}}}

{{{25y=100}}}

{{{y=100/25}}}

{{{highlight(y=4)}}}

go back to {{{x-11y=-41}}}...........(b), substitute {{{4}}} for {{{y}}}

{{{x-11*4=-41}}}

{{{x-44=-41}}}

{{{x=44-41}}}

{{{highlight(x=3)}}}

finally, go to  {{{2x-z=8}}}.....(2), substitute {{{3}}} for {{{x}}}

{{{2*3-z=8}}}

{{{6-8=z}}}

{{{highlight(z=-2)}}}


solutions:

{{{highlight(x=3)}}}

{{{highlight(y=4)}}}

{{{highlight(z=-2)}}}