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# 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.*

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- ANSWER

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.