How to solve two equations and three unknowns

How to solve two equations and three unknowns

Generally speaking, there are infinitely many solutions to this kind of equation, one of which is called free unknown quantity and can take any value
The solution is: x = (150-z) / 17, y = (350-8z) / 17, Z arbitrary

Three unknowns, three equations
a2+b2=r2
(a-1)2=r2
(a-1)2+(b-2)2=(r+1)2
As a result, I know, but I don't know how to calculate,

Three equations solve two unknowns
Can this form be solved@@

There may or may not be solutions
Take an extreme point
x=3
y=2
x+y=5
This group has a solution
x+y=2
2x+2y=4
3x+3y=6
This group doesn't know

Special solutions of two equations with three unknowns
What is the special solution
For example: solve positive integer solution or non negative integer solution

Select one of them as the free unknown quantity, make it = 0 or = 1, can be substituted into the original equations, so that it becomes the equations of two equations and two unknowns