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

1 Answer
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.