SOLUTION: Hello, Please help me solve this problem, thanks in advance. xy=1 x+y=2

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Question 372339: Hello,
Please help me solve this problem, thanks in advance.
xy=1
x+y=2
Found 2 solutions by mananth, neatmath:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
xy=1
/y
x=1/y
x+y=2
plug value of x
1/y + y = 2
(1+y^2)/y =2
multiply by y
(1+y^2)=2y
y^2-2y+1=0
(y-1)^2=0
square root
y-1=0
y =1
..
x+y=2
x+1=2
x=1
..
m.ananth@hotmail.ca

Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

xy=1 and x%2By=2

From the second equation, solve for y:

y=2-x

Substitute this value for y into the first equation.

x%2A%282-x%29=1

2x-x%5E2=1

-x%5E2%2B2x-1=0

x%5E2-2x%2B1=0

%28x-1%29%2A%28x-1%29=0

x-1=0

x=1

Substitute this value of x back into either original equation:

x%2By=2

1%2By=2

y=1

The only solution for this system of equations is x=1 and y=1, or the point (1,1).

Basically, the solution (1,1) is the intersection of the two functions:

y=-x+2 which is a line, and

y=1/x which is a curve (specifically, a hyperbola)

I hope this helps!