Friday, January 15, 2016
[AM_20160115SEAV] Simultaneous equations? Absolutely!
Problem / Question
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
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]
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
* 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