Non-linear system of eqtns

[Han]

purge(x,y,z);
eq1:=z*y - x^2 + y = -53;
eq2:=x^2 + y^2 - z = 47;
eq3:=x*y - x + z = -11;
soln:=fsolve([eq1,eq2,eq3],[x,y,z]=[1,5,0]);

Now check your answer:

subst(eq1,[x,y,z]=soln);
subst(eq2,[x,y,z]=soln);
subst(eq3,[x,y,z]=soln);

In each of these three cases, the left hand side should equal the right hand side (or be very close).

Finally, delete the variable 'soln' and the three equations (if you no longer need them):

purge(soln,eq1,eq2,eq3);

EDIT: forgot to mention this should be done in CAS view.