That really depends on the equation. In the simplest cases, you need to isolate the variable on one side - eliminate anything other than the variable, by doing the same operation on both sides. For example, if you have an "x + 3" on one side, subtract 3 on both sides, to remove the "3" from the left side.
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The answer depends on the kind of equation. Some cannot be solved analytically and only a numerical approximation is possible.
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.
You would solve them in exactly the same way as you would solve linear equations with real coefficients. Whether you use substitution or elimination for pairs of equations, or matrix algebra for systems of equations depends on your requirements. But the methods remain the same.