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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: aznboy50 on December 17, 2010, 04:57:43 pm

Title: Sketching Inequalities
Post by: aznboy50 on December 17, 2010, 04:57:43 pm: I know how to answer this question buy sketching. How would I find the answer algebraically?

The question is on page 40, question e) of Essentials Specialist

I can't upload the question due to the revolution...
Title: Re: Sketching Inequalities
Post by: dcc on December 17, 2010, 10:18:04 pm: Perhaps you could post the question for those of us who are not fortunate enough to own Essentials?
Title: Re: Sketching Inequalities
Post by: kamil9876 on December 17, 2010, 10:33:49 pm: Quote
I can't upload the question due to the revolution...

The revolution still allows typing and $Latex$
Title: Re: Sketching Inequalities
Post by: aznboy50 on December 18, 2010, 12:17:08 pm: x²-y² $\leq$ 1 and x²+y² $\leq$ 4

How would I solve this without the aid of graphs?
Title: Re: Sketching Inequalities
Post by: bblovee on December 18, 2010, 08:11:12 pm: looks like there is four intersections

you could always transpose the equations and solve for each quadrant
Title: Re: Sketching Inequalities
Post by: kamil9876 on December 18, 2010, 09:19:59 pm: By "solve" you mean you want to find the (x,y) that satisfy both of those inequalities. Too lazy to do the working, but I am guessing that you can't really find a better or simpler description of the set of all such (x,y) "algebraically". E.g: you can "solve" the equation 2x-4=0 to get the better description that x=2. But you can't really "solve" the equation x=2, since there is no better description for such possible values of x. However graphically you can find a description of the set in your case so I'm guessing the point of this exercise was to sketch?