Question 956003

{{{3x-4y-z=1}}}.....eq.1
{{{x-y+3z=3}}}.....eq.2
{{{3x-2y+2z=0}}}.....eq.3
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{{{3x-4y-z=1}}}.....eq.1
{{{3x-2y+2z=0}}}.....eq.3
-----------------------------------subtract

{{{3x-4y-z-(3x-2y+2z)=1-0}}}

{{{cross(3x)-4y-z-cross(3x)+2y-2z=1}}}

{{{-2y-3z=1}}}....solve for {{{y}}}

{{{-1-3z=2y}}}

{{{y=-(3/2)z-1/2}}}

{{{y=-1.5z-0.5}}}...substitute in


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

{{{x-(-1.5z-0.5)+3z=3}}}

{{{x+1.5z+0.5+3z=3}}}

{{{x+4.5z=3-0.5}}}

{{{x=-4.5z+2.5}}}....

go to {{{3x-4y-z=1}}}.....eq.1 substitute {{{x}}} and {{{y}}}

{{{3(-4.5z+2.5)-4(-1.5z-0.5)-z=1}}}...solve for {{{z}}}

{{{-13.5z+7.5-(-6z-2)-z=1}}}

{{{-13.5z+7.5+6z+2-z=1}}}

{{{-8.5z+9.5=1}}}

{{{-1+9.5=8.5z}}}

{{{8.5=8.5z}}}

{{{highlight(z=1)}}}

now we can find {{{x}}} and {{{y}}}

{{{x=-4.5z+2.5}}}
{{{x=-4.5*1+2.5}}}
{{{highlight(x=-2)}}}

{{{y=-1.5z-0.5}}}
{{{y=-1.5*1-0.5}}}
{{{highlight(y=-2)}}}