I have a system of two equations with three unknowns.
On solving, I got the following values. $$ y = a$$ $$x = (11-a)/2$$ $$z = (3-a)/2$$
How would I go about finding the number of solutions possible for this system? Also, is there a finite set of solutions?
Note: I made the original set of equations to solve another problem in which one has to find the number of seven digit numbers with sum of digits equal to 10 and made by using the digits 1, 2, 3 only.