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

First find the intersection of x+y=5 with x.y =2, by plugging in y= $\frac{2}{x}$ in the first equation. It would give ${x}^{2}$ -5x+2=0. On solving we have x= (5+$\sqrt{17}$)/2 and x=(5-$\sqrt{17}$)/2. The two points of intersection would be [ (5+$\sqrt{17}$)/2, 4/(5+$\sqrt{17}$)] and [5-$\sqrt{17}$)/2, 4/(5-$\sqrt{17}$)].