g/f = 1/10
(a*d*g + c*d*g) / (a*b*e +a*d*e) = 3/10
(c*g)/(a*e) = 4/10
You asked:
Solve the system of equations:\[\begin{aligned}\frac{g}{f} &= \frac{1}{10}\\\frac{a d g + c d g}{a b e + a d e} &= \frac{3}{10}\\\frac{c g}{a e} &= \frac{4}{10}\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}a &= \frac{5 c g}{2 e}\\b &= \frac{d \left(10 g + e\right)}{3 e}\\f &= 10 g\end{aligned}$$\(c\) is a free variable.
\(d\) is a free variable.
\(g\) is a free variable.