SOLUTION: 9x^2+25y^2=40.........(1) 3x+5y=6.........(2)

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Question 1066254: 9x^2+25y^2=40.........(1)
3x+5y=6.........(2)
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
9x%5E2%2B25y%5E2 = 40     (1)
3x%2B5y = 6         (2)


Express 3x = 6 - 5y from (2) and then substitute it into (1), replacing 9x%5E2 = %283x%29%5E2  (!!).  You will get

%286-5y%29%5E2+%2B+25y%5E2 = 40,

36+-+60y+%2B+25y%5E2+%2B+25y%5E2 = 40,

50y%5E2+-+60y+-+4 = 0.

y%5B1%2C2%5D = %2860+%2B-+sqrt%283600+%2B+4%2A4%2A50%29%29%2F100 = %2860+%2B-+10%2Asqrt%2844%29%29%2F100 = 0.6+%2B-+0.2%2Asqrt%2811%29.


Thus,  one solution is y%5B1%5D = 0.6+%2B+0.2%2Asqrt%2811%29, x%5B1%5D = %286-5y%5B1%5D%29%2F3 = %283+-+sqrt%2811%29%29%2F3.

The second solution is y%5B2%5D = 0.6+-+0.2%2Asqrt%2811%29, x%5B2%5D = %286-5y%5B2%5D%29%2F3 = %283%2Bsqrt%2811%29%29%2F3.