Making Assumptions Based on Number of Equations and Variable

[BernardK777]

The Algebra Strategy guide in Chapter 8 states that one should not make assumptions about sufficiency based on the number of variables and equations in the problem. As discussed in the chapter this is not safe because of combo and mismatch situations, but I was wondering if there is a time (or scenarios) when it is permissible to determine if a unique solution is possible based on the number of equations and variables. I'm a bit confused on this because in some cases I have found that this shortcut can be employed but not sure how to set of rule when it's okay.

Thanks.

[tim]

Here's the rule: if you have N *linearly independent* equations and N variables, that is sufficient (but not necessary) to be able to solve for all N variables. Linearly independent means that all equations are linear (adding up a constant times each variable gives you a constant) AND none of the equations are combinations of the other equations.

[RonPurewal]

Here's the rule: if you have N *linearly independent* equations and N variables, that is sufficient (but not necessary) to be able to solve for all N variables. Linearly independent means that all equations are linear (adding up a constant times each variable gives you a constant) AND none of the equations are combinations of the other equations.

^^ In other words, you can't tell by just looking, and you actually need to do the work.
(:

[RonPurewal]

Remember, in particular, that one of the major purposes of data sufficiency is to test cases in which "rules of thumb" don't work. So, if you're just taking a cursory glance at a system of equations and making quick assumptions about them, those assumptions will be wrong almost every single time.