\begin{question}{Ntuple}
% This question uses algorithmic variables.
\qutext{Find the exact solution of the following system of equations:
\begin{align*}
\var{a}x+\var{b}y&=\var{e}\\
\var{c}x+\var{d}y&=\var{f}
\end{align*}
\\
Your answer should be an ordered pair $(x,y)$.}
\answer{(\var{ans1},\var{ans2})}
% Note: The 'amsmath' package is needed to use the 'align' environment.
\code{$aa = range(2,6);
$b = range(2,6);
$c = range(2,6);
$d = range(2,6);
$e = range(2,6);
$f = range(2,6);
$det1 = int($aa*$d-$b*$c);
$a = int(if($det1,$aa,$aa+1));
$det = int($a*$d-$b*$c);
$x = int($e*$d-$f*$b);
$y = int($a*$f-$c*$e);
$ansx = $x/$det;
$ansy = $y/$det;
$ansxint = int($x/$det);
$ansyint = int($y/$det);
$detabs = int(abs($det));
$xabs = int(abs($x));
$yabs = int(abs($y));
$numx = int(if(lt($ansx,0),-$xabs,$xabs));
$numy = int(if(lt($ansy,0),-$yabs,$yabs));
$ans1 = if(eq($ansx,$ansxint),"$ansxint","$numx/$detabs");
$ans2 = if(eq($ansy,$ansyint),"$ansyint","$numy/$detabs");}
% The above code chooses random integer coefficients a, b, c, d, e,
% and f. a is modified if necessary so that the determinant of the
% system will be nonzero. The solution is then calculated using
% Cramer's Rule. Finally, care is taken to display the answer
% coordinates correctly.
\end{question}