Question 1197422


 {{{x + 2y - z = -5}}} .........eq.1
{{{y - 3z =-13}}}..............eq.2
{{{x - 3y + 2z = 12}}}............eq.3
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start with
{{{y - 3z =-13}}}..............eq.2, solve for {{{y}}}


{{{y  =3z-13}}}..............eq.2a

go to

{{{x + 2y - z = -5}}} .........eq.1, substitute {{{y}}}

{{{x + 2(3z-13)- z = -5}}} 

{{{x + 6z-26- z = -5}}} 

{{{x + 5z = -5+26}}} ........., solve for {{{x}}}

{{{x = 21-5z}}}...........eq.1a

go to

{{{x - 3y + 2z = 12}}}............eq.3, substitute {{{x}}} and {{{y}}}

{{{21-5z - 3(3z-13) + 2z = 12}}}........., solve for {{{z}}}

{{{21-5z - 9z+39+ 2z = 12}}}

{{{-12z+60 = 12}}}

{{{-12+60 = 12z}}}

{{{48 = 12z}}}

{{{z=48/12}}}

{{{z=4}}}

go to

{{{y  =3z-13}}}..............eq.2a, substitute {{{z}}}

{{{y  =3*4-13}}}

{{{y  =12-13}}}

{{{y  =-1}}}

go to

{{{x = 21-5z}}}...........eq.1a, substitute {{{z}}}

{{{x = 21-5*4}}}

{{{x = 21-20}}}

{{{x = 1}}}

solution:

{{{x = 1}}}

{{{y  =-1}}}

{{{z=4}}}