The basic idea is that you need to carry out the same operations on both sides of an equation.
In a scale, assuming you want to keep it balanced, if you add 3 kg. on the left side, you also need to add 3 kg. on the right side.
With an equation, the situation is similar; except that you can not only add and take away (add and subtract), but also (with certain limitations and caveats which you should learn) multiply both sides by the same number or term, divide both sides, square, take square roots, take trigonometric and inverse trigonometric functions, etc.
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Tell me the equations first.
You need as many equations as you have variables.
You can solve the system of equations with three variables using the substitute method, or using matrix operations.
If you don't learn to solve equations then guess and check is the only way to arrive at new information.
Simultaneous equations are where you have multiple equations, often coupled with multiple variables. An example would be x+y=2, x-y=2. To solve for x and y, both equations would have to be used simultaneously.