<PRE><B>Question 372339</B>
&lt;br&gt;&lt;font face=&quot;Tahoma&quot;&gt;{{{xy=1}}}  and  {{{x+y=2}}} &lt;br&gt;

From the second equation, solve for y:&lt;br&gt;

{{{y=2-x}}}&lt;br&gt;

Substitute this value for y into the first equation.&lt;br&gt;

{{{x*(2-x)=1}}}&lt;br&gt;

{{{2x-x^2=1}}}&lt;br&gt;

{{{-x^2+2x-1=0}}}&lt;br&gt;

{{{x^2-2x+1=0}}}&lt;br&gt;

{{{(x-1)*(x-1)=0}}}&lt;br&gt;

{{{x-1=0}}}&lt;br&gt;

{{{x=1}}}&lt;br&gt;

Substitute this value of x back into either original equation:&lt;br&gt;

{{{x+y=2}}}&lt;br&gt;

{{{1+y=2}}}&lt;br&gt;

{{{y=1}}}&lt;br&gt;

The only solution for this system of equations is x=1 and y=1, or the point (1,1).&lt;br&gt;

Basically, the solution (1,1) is the intersection of the two functions:&lt;br&gt;

y=-x+2 which is a line, and&lt;br&gt;

y=1/x which is a curve (specifically, a hyperbola)&lt;br&gt;

I hope this helps!&lt;br&gt;</PRE>