Re: Is there a solution?

On 4/5/05 11:21 PM, DP wrote: 
Let x(t) = t
then
y(t) = ((-at+d)/(b+ct))
Solve for t based on selected a, b, c, d integers

Okay. So let's say (a,b,c,d) = (1,2,3,4), so that our equation reads x+2y+3xy=4. You said solve for t. I get:

t = (4-2y) / (1+3y)

(writing y for y(t)).

Since t = x(t), this looks like a hyperbola (in both first and 3rd quadrants) with the origin shifted a bit.

((-at+d)/(b+ct)) = 0

???? Why are we equation it to zero? If I do that, it will find out where the curve crosses the x-axis. And that's going to be where the numerator == 0, right? Now how do I work out the integer solutions, or whether there exists an integer solution?
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