Question 768644

{{{x+y+z=4}}}........eq.1
{{{x-y+4z=18}}}.......eq.2
{{{2x+y+z=5}}}........eq.3
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{{{x+y+z=4}}}........eq.1
{{{x-y+4z=18}}}.......eq.2
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{{{x+y+z+x-y+4z=4+18}}}

{{{2x+5z=22}}}......solve for {{{x}}}

{{{2x=22-5z}}}

{{{x=11-(5/2)z}}}......eq.1a


{{{2x+y+z=5}}}........eq.3 plug in {{{x}}}

{{{2(11-(5/2)z)+y+z=5}}}........eq.3

{{{22-5z+y+z=5}}}.......solve for {{{y}}}

{{{y=5z-z+5-22}}}
{{{y=4z-17}}}.............eq.3a

go to eq.1 and substitute {{{x}}} from eq.1a and {{{y}}} from eq.3a


{{{11-(5/2)z+4z-17+z=4}}}........eq.1...solve for {{{z}}}


{{{-(5/2)z+5z-6=4}}}

{{{-(5/2)z+5z=4+6}}}...multiply by {{{2}}}

{{{-5z+10z=20}}}

{{{5z=20}}}

{{{highlight(z=4)}}}

now find {{{x}}} and {{{y}}}

{{{x=11-(5/2)z}}}......eq.1a

{{{x=11-(5/2)*4}}}

{{{x=11-5*2}}}

{{{x=11-10}}}

{{{highlight(x=1)}}}

{{{y=4z-17}}}.............eq.3a

{{{y=4*4-17}}}

{{{y=16-17}}}

{{{highlight(y=-1)}}}