Friday, January 15, 2016

[AM_20160115SEAV] Simultaneous equations? Absolutely!

Problem / Question

Introduction
     This question was from a Facebook group not dedicated to “Singapore math”.  The thing is, mathematics is really an international experience, especially with modern social media.
     Simultaneous equations can pose a challenge to students, but this one is absolutely more challenging, because of the absolute value.

The Absolute Value

Strategy
     The problem is: we do not know whether each of  x  and  y  is negative or otherwise.  That potentially raises complications.  There seems to be  4  cases to check.  However, by making assumptions  [H08]  separately and checking for contradictions [H07], we can narrow down the possibilities.  [H10]  Finally, we can simplify the problem to a regular pair of simultaneous linear equations   [H10]  and solve it by the method of elimination.  [H10, H11]

Solution


H04. Look for pattern(s)        [deciding what to eliminate]
H07. Use guess and check     [is x negative?  is  y negative?]
H08. Make suppositions        [is x negative?  is  y negative?]
H10. Simplify the problem
H11. Solve part of the problem
H13* Use Equation / write a Mathematical Sentence


Suitable Levels
Lower Secondary Olympiad
GCE ‘O’ Level Additional Mathematics, “IP Mathematics” (challenge)
* other syllabuses that involve simultaneous equations and absolute values
* any precocious or independent learner who wants his/her mind tickled




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