MATLAB: Solve fails to find a solution for trivial linear system

Question

I'm trying to find the value of G in the following set of equations by code:

clear all; clc;
syms R T S u yr y B A G
eq1 = R*u == T*yr - S*y;
eq2 = y == (B/A)*u;
eq3 = y == G*yr;
solve([eq1,eq2,eq3], G)

However, solve fails with an empty solution set, although this system has a trivial answer.

It's easy to see how it can be done, from eq1:

u == (T*yr - S*y)/R

From eq2:

y == (B/A)*(T*yr - S*y)/R

Thus:

y = yr*(B*T)/(A*R + B*S)

Finally, from eq3:

G = (B*T)/(A*R + B*S)

I can't understand why solve fails in this case. I appreciate any help I can get.

Answer 1

Actually it is just a matter of telling it all three variables to solve for:

solve(eq1, eq2, eq3, y, u, G)