Is this a homework question ?
If it is there will be some rules - like perhaps they want you to do it from first principles ?
If not then you could use LTSpice (free) but you will need actual values for the resistors.
I don't know of any free symbolic circuit simulators.
Tell us a bit more about what you are trying to do and it will be possible to offer advice.
I'm sorry but I'm (nearly) as puzzled as you - I can't work out what the voltages in the equations refer to - there are two transistors and I can't tell which one Veq or Vcq refer to. Your tutor has made the fundamental error (and you can tell them I said so!!) of using terms in the equations which can't be identified in the diagram.
I think the equations are meant to refer to the second transistor and the first line is saying that it would be nice to set the emitter voltage of Q2 at 10% of the supply voltage - this is a reasonable rule of thumb way of picking it.
The second is saying that the quiescent operating point for Q2 should result in Q2 collector voltage being half way between the emitter voltage and the supply - again this is reasonable since it would allow the output of the amplifier to swing almost equally positive and negative.
The third line just expands the equation in the second line.
From the 0.55Vc = 8.25V it looks as if the supply is 15.0V.
There isn't enough information to solve the circuit completely, you would need to know Vz (by the way - this is a poor design (you should never use a zener diode like that !!! (because the current in it will be too low for it to zener properly))) . You would also need to have some idea of the operating currents for the transistors etc.
You can estimate the Vb, e and c on Q1 by assuming the Vbe voltage of Q1 and Q2 (somewhere between 0.5 and 0.6V will do).
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I believe your teacher has given you this homework so that you can get used to applying the right models for the components when doing your circuit hand analysis. Very often those circuits have very little use in real world electronics, nevertheless you can learn very good lessons by resolving them.
To carry the DC analysis (so you can calculate the biasing of the components, and the Q point, which you later use to calculate the small signal parameters for the transistor AC model), you need to start by making some assumptions on the transistors and the diode biasing state. The DC models for the transistor are active region, saturation region and off region, while for the zener diode you have a forward region, off region and a reverse (or zener) region. All you have to do is starting by assuming an operating region for those components, replace the components with their respective DC models and do your circuit analysis. Once you calculated all the voltages and currents, you need to verify that the results agree with your assumptions. If so, you don't need to do anything else. If the results violate your assumptions, then you need to change some of the assumptions, replace the models with the new ones and do the calculations again. You keep repeating the process till you find the right assumptions.
The assumption about the Vc=Vcc/2 is typical for a transistor biased in active region: this is done to make sure you get the maximum dynamic available for the AC output signal. As such, usually it refers to the transistor at the final stage of the multistage amplifier.
Please, don't take this the wrong way, I'm happy to help you, but for the time being I don't really want to add much more, as I think it would defeat the object of this homework if someone else resolves the circuit for you.
Have a go at the circuit, and I'm sure you will be able to solve it yourself. If you get stuck again, let me know.