10 solutions
x,y,z>0 x+y+z=6 => x,y,z<5 x=1=> y+z=5 => y,z=1,4/2,3/3,2/4,1 --> 4 solutions x=2=> y+z=4 => y,z=1,3/2,2/3,1 --> 3 solutions x=3=> y+z=3 => y,z=1,2/2,1 --> 2 solutions x=4=> y+z=2 => y,z=1,1 --> 1 solution 4+3+2+1=10 solutions
How many integer solutions are there to the system of equations below and which are those solutions?
x^2+y-z = 42 x+y^2-z = 18