Question 887471
A guess about what your fancy script "c" mean...?....?  Not sure, but the system of equations can be examined.


{{{x^2-y^2=9}}} is a hyperbola.  Solve the other equation for either variable and substitute.

{{{x=2y-3}}};
{{{(2y-3)^2-y^2=9}}}
{{{4y^2-12y+9-y^2=9}}}
{{{3y^2-12y=0}}}
{{{y^2-4y=0}}}
{{{y(y-4)=0}}}
Either {{{y=0}}} Or y-4=0, {{{y=4}}}


The x corresponding to {{{y=0}}} should be {{{x=2*0-3=-3}}}, for the point (-3,0).


The x corresponding to {{{y=4}}} is {{{x=2*4-3=5}}} for the point (5,4).


These can be both considered Complex solutions as well as Real solutions, but the way you describe you fancy c, does not seem to mean Complex.  The solutions are also Real because they contain no imaginary part.