Question 1050346
Say you're given the triple (1,2,3).
So then,
{{{3x=3(1)=3}}}
{{{5y=5(2)=10}}}
{{{2z=2(3)=6}}}
So then I can say,
{{{3x+5y+2z=3+10+6}}}
{{{3x+5y+2z=19}}}
So there's one equation. 
Another would be {{{x+y+z=6}}}
Another would be {{{x+y-z=0}}}
Just avoid making multiples of another equation.
Such as,
{{{6x+10y+4z=38}}}
.
.
.
So then those three equations have the solution (1,2,3).