Question 1175220
{{{x -2y + z = -3}}} .....eq.1
{{{y + 2z = -5}}}.....eq.2
{{{x + y + 3z = -6}}}.....eq.3
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 {{{y + 2z = -5}}}.....eq.2, solve for {{{y}}}

 {{{y  =- 2z -5}}}.........a)


go to

{{{x -2y + z = -3}}} .....eq.1....substitute {{{y}}}
{{{x -2(- 2z -5) + z = -3}}}
{{{x +4z +10 + z = -3}}}
{{{x = -5z-13}}}........b)


go to

{{{x + y + 3z = -6}}}.....eq.3...substitute {{{y}}}
{{{x - 2z -5 + 3z = -6}}}
{{{x  -5 + z = -6}}}
{{{x  = 5-6-z}}}
{{{x  = -1-z}}}........c)


from b) and c) we have

{{{ -5z-13=-1-z}}}.....solve for {{{z}}}
{{{ 1-13=5z-z}}}
{{{ -12=4z}}}
{{{ z=-12/4}}}
{{{ z=-3}}}


go to

 {{{y  =- 2z -5}}}.........a)..substitute {{{z}}}
{{{y  =- 2*(-3) -5}}}
{{{y  =6 -5}}}
{{{y  =1}}}

go to

{{{x  = -1-z}}}........c)..substitute {{{z}}}
{{{x  = -1-(-3)}}}
{{{x  = -1+3}}}
{{{x  = 2}}}



solution set:
{{{x = 2}}}
{{{ y = 1}}}
{{{ z = -3}}}