SOLUTION: x+y=11 x*y=11 find x,y??

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Question 683326: x+y=11
x*y=11
find x,y??
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x+y=11 --> y = 11-x
x*y=11
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Sub for y in the 2nd eqn
x(11-x) = 11
x%5E2+-+11x+%2B+11+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-11x%2B11+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-11%29%5E2-4%2A1%2A11=77.

Discriminant d=77 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+77+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+77+%29%29%2F2%5C1+=+9.88748219369606
x%5B2%5D+=+%28-%28-11%29-sqrt%28+77+%29%29%2F2%5C1+=+1.11251780630394

Quadratic expression 1x%5E2%2B-11x%2B11 can be factored:
1x%5E2%2B-11x%2B11+=+%28x-9.88748219369606%29%2A%28x-1.11251780630394%29
Again, the answer is: 9.88748219369606, 1.11251780630394. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-11%2Ax%2B11+%29

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The 2 solutions are for x & y