SOLUTION: if x^2 + xy= 12 and xy + y^2 = 6 find x and y note : x>0

Question 994121: if x^2 + xy= 12 and xy + y^2 = 6 find x and y
note : x>0
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

x^2 + xy = 12,       (1)
xy + y^2 =  6.       (2)


Add two equations (1) and (2). You will get


 = , or  = , or x + y = +/- .      (3)


Next, distract the equation (2) from the equation (1). You will get


 = , or (x+y)*(x-y) = 6.                                (4)


By combining (5) and (6), you have two linear systems of two equations in two unknowns


,        and     .


Simplify right sides:


,        and     .


First of these two systems has the solution x = , y = .

The second system has negative solutions x = -, y = -.


According to the condition, only the pair x = , y =  does suit.

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