# I Finding number of solutions for a system of equations?

1. Aug 12, 2016

### kochibacha

Is there any general theorem on finding number of solutions to this system of equations

(D e^(-k (a - t)) (1 - e^-kt) (1 - e^(-a k n)))/((1 - e^(-a k)) k t v) = S

(G e^(-k (a - t)) (1 - e^-kt) (1 - e^(-a k n)))/((1 - e^(-a k)) k t v) = T

where k,v are variables and others are constant

*edited equations

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Last edited: Aug 12, 2016
2. Aug 12, 2016

### Staff: Mentor

The two equations look identical. If S=T that is fine, just a bit redundant. It is easy to solve for v(k) then, which has a unique solution everywhere apart from k=0 where the equation cannot be satisfied.

3. Aug 12, 2016

### kochibacha

thanks for the fast reply. The problem was actually Mathematica cannot solve these system of equations (picture attached) so I used Excel Solver to find k,v satisfying those two equations. I just wonder that the k,v that I got are the only real number solutions to this system.

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4. Aug 12, 2016

### Staff: Mentor

There is no solution. Your equations are "250 * something = 50 && 375 * something = 80", which quickly leads to a contradiction.