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Question

If 3x+y+2xy=2 and 9x+y4xy=1 then

(a) x=12,y=32 (b) x=52,y=12 (c)x=32,y=12 (d) x=12,y=52

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Solution

3x+y+2xy=29x+y4xy=1Put 1x+y=u and 1xy=v3u+2v=2(1)9u4v=1(2)(1)×39u+6v=6(3)(3)(2)10v=5v=510=123u+2v=23u=22u22×12=21=13u=1u=131x+y=u=13x+y=31xy=v=12xy=22x=5x=52y=352=652=12 x=52 and y=12


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