Wednesday, 24 August 2016

solving absolute value equation 2




My question is : Solve simultaneously-



{|x1|+|y2|=1y=3|x1|



I tried to solve this question by the method told by Marvis as I had understood that method (its here: Solve an absolute value equation simultaneously



But the solution set i got for the above question is not correct.
My solution was: y2, and x=3 or x=y-2.
I would like to know the final correct solution.



Answer



We shall proceed on similar lines as the answer here.



You have that |x1|+|y2|=1. This gives us that |x1|=1|y2|.

Plugging this into the second equation gives us y=3(1|y2|)=2+|y2|

This gives us that y|y2|=2.

If y>2, then we get that yy+2=2,
which is true for all y>2.



If y2, then we get that y+y2=2y=2

Hence we get that y2
From the second equation, we get that |x1|=3y

Since |x1|0, we need 3y0
This means that y3. Hence, we have that 2y3.




If x1, then x1=3yx=4y. Note that since y[2,3], x=4y1.



If x<1, then x1=y3x=y2. Note that since y[2,3], x=y2<1.



Hence, the solution set is given as follows. 2y3 and x=4y or y2


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