By eliminating or substituting one of the variables in the two equations in order to find the value of the other variable.
When this variable is found then substitute its value into the original equations in order to find the value of the other variable.
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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.
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.