Question 559331
x+y =5

xy = 5
x=5/y

substitute x in first equation
5/y +y =5

multiply equation by y
5+y^2=5y
y^2-5y+5=0

y^2-5y=-5

complete the square on the left side
y^2-5y+25/4=-5+25/4
(y-5/2)^2= 5/4
take the square root
y-5/2 = +/- sqrt(5)/2
y= 5/2 + sqrt(5)/2 = (5+sqrt5)/2
y=3.618
OR
y= 5/2 -sqrt(5)/2
y= (5-sqrt(5))/2
y=1.38