How do you solve the system of equations with absolute value abs(x+y)=5 and abs(x*y)=2?

1 Answer
bp
Apr 2, 2015

|x+y| =5 would represent two straight lines x+y=5 and x+y = -5. Similarly |x.y| =2 will represent two asymptotic curves x.y=2 and x.y= -2.

First find the intersection of x+y=5 with x.y =2, by plugging in y= 2/x in the first equation. It would give x^2 -5x+2=0. On solving we have x= (5+sqrt17)/2 and x=(5-sqrt17)/2. The two points of intersection would be [ (5+sqrt17)/2, 4/(5+sqrt17)] and [5-sqrt17)/2, 4/(5-sqrt17)].

There will be in all 8 points of intersection which each line would have with each curve, which can be calculated like wise.

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