Question 1153199

this calculator is really good:

https://www.mathportal.org/calculators/system-of-equations-solver/system-3x3.php


{{{2x+y-3z=1}}}.......1)
{{{x-2y-z=3}}}.......2)
{{{x+8y-3z=-7}}}.......3)
--------------------


{{{x-2y-z=3}}}.......2)
{{{x+8y-3z=-7}}}.......3)
-------------------------subtract

{{{x-2y-z-(x+8y-3z)=3-(-7)}}}

{{{cross(x)-2y-z-cross(x)-8y+3z=3+7}}}

{{{-10y+2z=10}}}

{{{2z=10y+10}}}

{{{10y=2z-10}}}

{{{y=z/5-1}}}.......................1a)



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

{{{2x+z/5-1-3z=1}}}

{{{2x+z/5-15z/5=1+1}}}

{{{2x-14z/5=2}}}

{{{2x=14z/5+2}}}

{{{x=7z/5+1}}}..................1b)



{{{x-2y-z=3}}}.......2)....substitute {{{x}}} and {{{y}}}

{{{7z/5+1-2(z/5-1)-z=3}}}

{{{7z/5+1-2z/5+2-z=3}}}

{{{5z/5-z=3-1-2}}}

{{{z-z=3-3}}}

{{{0=0}}}-> is always true; so the system has {{{infinitely}}}{{{ many}}} solutions 

The solutions to the system of equations are: {{{x=7z/5+1}}}, {{{y=z/5-1}}}