Solving a system of equations (it give no solution in the software)

Question

Why does the following equation not give a solution:

Solve[{(-502375/10^5)*(-R2/R1) == x, (49539/10^4)*(-R2/R1) == -x, 
  R1 > 0 && R2 > 0 && 0 < x <= 10}, {R1, R2}]

I want to solve (for $R1$ and $R2$):

$$\frac{-502375}{10^5}\cdot\left(-\frac{R2}{R1}\right)=x,\frac{49539}{10^4}\cdot\left(-\frac{R2}{R1}\right)=-x$$

Where $R1>0$, $R2>0$ and $0<x\le10$

Answer 1

Simply because there's no solution. If you add your equations, you will end up with something of the form $a \dfrac{R_2}{R_1}=0$, with $a\neq 0$. So $ \dfrac{R_2}{R_1}=0$, and $R_2=0$. Since you want $R_2>0$, there's no solution.