System of Equations with a changing variable

I need help with syntax to solve a system of equations. There are 3 equations, with 3 unknowns, and a fourth variable that ranges from 5-15. An example of one of these equations would be

1)10x/(5+r^2)+34y/(7+r^2)+23z/(2+r^2)=…
2)...
3)...

Where xyz are what will be solved for, for every value of r between 5-15, and then the results being graphed.

Any help with the setup and syntax for this would be much appreciated.

Eric