Question 106425
if we have this matrix:


[1,1,1][x]= [100]
[5,-3,0][y]= [10]
[0,3,4] [z]= [290]



the system of equations is:


  {{{x  +  y  +  z  = 100}}}
{{{5x  - 3y          =  10}}}
{{{ 3y  + 4z = 290}}}


and a real-world word problem could be:


Three detectives named Mr. Clueless (let the number of cases the he has solved be {{{x}}}), Mr. Confused (let the number of cases the he has solved be {{{y}}}), and Mr. Smarty Pants (let the number of cases the he has solved be {{{z}}}) all together have solved {{{100}}} {{{cold}}}{{{ cases}}}.
Since Mr. Clueless is kind of "{{{slow}}}", his {{{quintuple}}} number of cases is {{{10}}} less then {{{triple}}} number of Mr. Confused cases. We also know that a {{{sum }}}of {{{triple}}} number of  Mr. Confused cases and {{{quadruple}}} number of Mr. Smarty Pants cases is {{{290}}}.
What a number of {{{cold}}}{{{ cases}}} have each of them solved?