Luke53 wrote:x/10 = y/14 = z/35 = 1/(10x + 14y + 35z)
How to solve this system?
It won't be nice and easy, since the system isn't linear. However, you can create three equations in three variables, which should be solveable.
I would start by restating two of the variables in terms of the other. For instance, you could use "x/10 = y/14" and "x/10 = z/35" to restate y and z in terms of x. Then plug these into the final equation, "x/10 = 1/(10x + 14y + 35z)", and solve for the value(s) of x. Then back-solve for y and z.