You cannot work a simultaneous equation. You require a system of equations. How you solve them depends on their nature: two or more linear equations are relatively easy to solve by eliminating variables - one at a time and then substituting these values in the earlier equations. For systems of equations containing non-linear equations it is simpler to substitute for variable expression for one of the variables at the start and working towards the other variable(s).
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There are several ways to do that: for example substitution, or subtracting one equation (or a multiple of one equation) from the other.
Another straight line equation is needed such that both simultaneous equations will intersect at one point.
p q and p q cannot be a useful part of a system of simultaneous equations since they are the same!
Yes, for solving simultaneous equations.
That depends on what type of equation it is because it could be quadratic, simultaneous, linear, straight line or even differential
Without any equality signs the given terms can't be considered to be simultaneous equations.