SOLUTION: Solve the system of equations x+y=2 and x^2+2y^2=11

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Question 987802: Solve the system of equations x+y=2 and x^2+2y^2=11
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve the system of equations

system%28x+%2B+y+=+2%2C%0D%0Ax%5E2+%2B+2y%5E2+=+11%29.
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Express x from the first equation  x = 2-y  and substitute it into the second equation.  You will get

%282-y%29%5E2 + 2y%5E2 = 11,

4+-+4y+%2B+y%5E2 + 2y%5E2 - 11 = 0,

3y%5E2+-+4y+-+7 = 0,

y%5B1%2C2%5D = %284+%2B-+sqrt+%284%5E2+%2B+4%2A3%2A7%29%29%2F6 = %284+%2B-+sqrt+%2816+%2B+84%29%29%2F6 = %284+%2B-+sqrt+%28100%29%29%2F6 = %284+%2B-+10%29%2F6.

y%5B1%5D = %284+%2B+10%29%2F6 = 14%2F6 = 21%2F3;

y%5B1%5D = %284+-+10%29%2F6 = %28-6%29%2F10 = -1.