SOLUTION: Please help me show a step by step solution to x^2+y^2=13 xy=6

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Question 930685: Please help me show a step by step solution to
x^2+y^2=13
xy=6
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Please help me show a step by step solution to
x^2+y^2=13
xy=6
x%5E2+%2B+y%5E2+=+13 ------ eq (i)

xy+=+6______x+=+6%2Fy ---------- eq (ii)

%286%2Fy%29%5E2+%2B+y%5E2+=+13 -------- Substituting 6%2Fy for x in eq (i)

36%2Fy%5E2+%2B+y%5E2+=+13

36+%2B+y%5E4+=+13y%5E2 -------- Multiplying by LCD, y%5E2

y%5E4+-+13y%5E2+%2B+36+=+0

%28y%5E2+-+4%29%28y%5E2+-+9%29+=+0

(y - 2)(y + 2)(y -3)(y + 3) = 0

Thus: y = 2,  or   y = - 2, or   y = 3,   or    y = - 3



If y = 2

x+=+6%2F2, or 3

When highlight_green%28system%28x+=+3%2C+y+=+2%29%29



If y = - 2

x = 6%2F%28-+2%29, or - 3

When highlight_green%28system%28x+=+-+3%2C+y+=+-+2%29%29



If y = 3

x = 6%2F3, or 2

When highlight_green%28system%28x+=+2%2C+y+=+3%29%29



If y = - 3

x = 6%2F%28-+3%29, or - 2

When highlight_green%28system%28x+=+-+2%2C+y+=+-+3%29%29

You can do the check!! 

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