Question 1074725
x, y, z

Assumption made here is {{{x<y}}}.


{{{system(x+y+z=20,y-x=5,z=4(x+y))}}}


(corrected)---

Substituting for z,
{{{system(x+y+4(x+y)=20,-x+y=5)}}}


{{{system(x+y=4,-x+y=5)}}}
The system here ready for use of Elimination Method.
ADD:  {{{2y=9}}}
{{{highlight_green(y=9/2)}}}
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SUBTRACT:  {{{-2x=1}}}
{{{highlight_green(x=-1/2)}}}
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Use x and y to find z.





-
(posted earlier -  incorrect -
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{{{x+y=20-z}}}    From first equation
{{{z=4(20-z)}}}   Substituted into equation #3
{{{z=80-4z}}}
{{{3z=80}}}-----MISTAKE... All the rest below is wrong...
{{{z=80/3}}}

{{{x+y+80/3=20}}}
{{{3x+3y+80=60}}}
{{{3x+3y=-20}}}

Simpler system in just x and y
{{{system(3x+3y=-20,-x+y=5)}}}

{{{(3x+3y)+(-3x+3y)=-20+5}}}
{{{6y=-15}}}
{{{2y=-5}}}
{{{y=-5/2}}}

{{{y-x=5}}}
{{{y-5=x}}}
{{{x=-5/2-5}}}
{{{x=-5/2-10/2}}}
{{{x=-15/2}}}