# Solve an algebraic equation

I want to obtain some positive x and y which satisfy the equation

0.01 x^2 - 0.01 x^3 - 0.01 x + 0.01 x^2 + y == 0


I have written:

Solve[0.01 x^2 - 0.01 x^3 - 0.01 x + 0.01 x^2 + y == 0 && x > 0 && y > 0, {x, y}]


But it returns errors:

Solve::svars: Equations may not give solutions for all "solve" variables. >> Solve::ratnz: "Solve was unable to solve the system with inexact coefficients. The answer was obtained by solving a corresponding exact system and numericizing the result. >>

Where am I doing wrong?

• You have received excellent answers below, but nonetheless I think it would be best to point out that, in the future, you should mention exactly what errors you obtain, when you ask a question. This helps those answering the question more appropriately. – MarcoB Dec 7 '15 at 2:47

expr = 0.01 x^2 - 0.01 x^3 - 0.01 x + 0.01 x^2 + y == 0 && x > 0 && y > 0 //
Rationalize;

Solve[expr, {x, y}]

(*  Solve::svars: Equations may not give solutions for all "solve" variables. >>  *)

(*  {{y -> ConditionalExpression[
(1/100)*(x - 2*x^2 + x^3),
0 < x < 1 || x > 1]}}  *)

Reduce[expr, {x, y}]

(*  (0 < x < 1 || x > 1) &&
y == (1/100)*(x - 2*x^2 + x^3)  *)


Use FindInstance for examples of numerical values

FindInstance[expr, {x, y}, Reals, 5]

(*  {{x -> 267/502,
y -> 589803/506024032},
{x -> 416, y -> 716456},
{x -> 197, y -> 1891988/25},
{x -> 268, y -> 4776363/25},
{x -> 335/502,
y -> 1868563/2530120160}}  *)

And @@ (expr /. %)

(*  True  *)


Or for Integers

FindInstance[expr, {x, y}, Integers, 5]

(*  {{x -> 96, y -> 8664},
{x -> 32761, y -> 351596817936},
{x -> 42225, y -> 752815242816},
{x -> 26800, y -> 192473955468},
{x -> 17256, y -> 51377155914}}  *)

And @@ (expr /. %)

(*  True  *)


If you want only the points then try this:

points = Table[{x /.
NSolve[0.01 x^2 - 0.01 x^3 - 0.01 x + 0.01 x^2 + y == 0 &&
x > 0][], y}, {y, 0, 10, .5}];
ContourPlot[
0.01 x^2 - 0.01 x^3 - 0.01 x + 0.01 x^2 + y == 0, {x, 0, 10}, {y, 0,
10}, Epilog -> Point[points]] 