Hi,
I encountered the following question in the PrepSwift Quant Quiz #5:
In this question, since it is asking the number of “distinct three-variable” equations, it can be 1, 2, or 3, correct? In order to solve for a,b,c in 3 different equations, there can be the set of equations as follows:
a+b = 10
2a + 3b + c = 4
3a + 5b + 5c = 8
The above set of equations will solve for a,b,c and yet it has 2 “distinct three-variable” equations, since the first equation only has a,b and not c.
Similarly, for the number of “distinct four-variable” equations, it can be 1, 2, 3, or 4 as the answer.
So, then shouldn’t the correct answer be D? The answer key says B.
Thanks for the help in advance!
Well a + b = 10 wouldn’t be allowed since they asked for three variable equations.
However, I will say that the question is ambiguous because the notion of “solve” isn’t really clear in the given context and based on the answer “distinct” here is supposed to be synonymous to linear independence (which it obviously isn’t w/o additional context).
I guess you can just skip the question, it shouldn’t be that important.
Let’s just say that the key takeaway is that when you’re solving most of those algebra problems and if you have say n unknowns, then you’d generally be looking for n equations to link all said variables in some way.
I think that’s the idea indeed - do you think that isn’t implied in the question? Of course, we cannot directly use the “linear independence” term without making the question unwieldy.
Yeah cuz like x + y = 1 and 2x + 2y = 2 are distinct equations, but not really distinct in a sense that would be useful.
That’s fair, perhaps you could imply that the system has unique solutions and so one isn’t left wondering what to do for 0 or infinitely many solutions at the very least.
