What software to use to solve system of equation for one variable with another variable and other constants?

Question

I am trying to solve a set of four equations. There are some variables expressing known values, and there are also four unknowns. I want one specific variable to be expressed in terms of another and the constants.

I tried doing this by hand but it was too messy. What are the commands to do so on Mathematica, Maple, or WolframAlpha (or any other software)?

These are the equations:

$$V_{1a}*A + V_{1b}*B = V_f$$ $$V_{0a} + V_{0b} = V_{1a}*A + V_{1b}*B$$ $$V_{0a} - V_{0b} - X*(V_{0a}+V_{0b}) = V_{1a}+V_{1b} $$ $$V_f = V_{1a}*A - V_{1b}*B - \frac{(V_{1a}*A + V_{1b}*B)}{Z} $$

I want $V_f$ in terms of only $V_{0a}$ and the constants (X, A, and B). What would be the best way to get this?

Answer 1

Try this in mathematica:

Solve[
    {
        V1a A+V1b B==Vf,
        V0a+V0b==V1a A+V1b B,
        V0a-V0b-X(V0a+V0b)==V1a+V1b,
        Vf==V1a A-V1b B-(V1a A+V1b B)/Z
    },
    {Vf,V0b,V1a,V1b}
]

This forces mathematica to give $V_f$ in terms of $A,B,X,V_{0a},Z$ since other variables are included in the solve list {Vf,V0b,V1a,V1b}.