Question

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

Answer 1

|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.