Find the values of x and y. x^2 + 4y^2 =40 xy=6

Considering x and y as two positive real numbers.

From equation 2, we can make x the subject of the formula 

Substituting equation 3 into equation 1, we get

Multiplying both sides by y², we get

Collecting the like terms

On dividing both sides by 4, it results to

 is a factor in and it can be expanded as (y+1)(y-1)

Furthermore,

So,

Substituting y=3 in equation 2xy=6  Y=6/x, When x=3 , y=6/3 y=2                           when x=1, y=6/1  y=6                           when x= -3 , y=6/-3 Y=-2 

                           When x=-1, y=6/-1 Y=-6 

Reference

Ostrowski, A. M. (2016). Solution of Equations and Systems of Equations: Pure and Applied Mathematics: A Series of Monographs and Textbooks (Vol. 9). Elsevier.