SOLUTION: Is it possible for an equation to have a solution but no graph? Here's the problem: 2/x + 3/y = 2, 4/x - 9/y + 1. The solution I got was x=2, y=3. But I don't know what to do when

Algebra ->  Systems-of-equations -> SOLUTION: Is it possible for an equation to have a solution but no graph? Here's the problem: 2/x + 3/y = 2, 4/x - 9/y + 1. The solution I got was x=2, y=3. But I don't know what to do when       Log On


   

Question 815483: Is it possible for an equation to have a solution but no graph? Here's the problem: 2/x + 3/y = 2, 4/x - 9/y + 1. The solution I got was x=2, y=3. But I don't know what to do when getting x and y intercept since there's undefined. (like 3/0 and 9/0)
Found 2 solutions by Alan3354, jsmallt9:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Is it possible for an equation to have a solution but no graph?
I don't think so.
-----------
Here's the problem: 2/x + 3/y = 2, 4/x - 9/y + 1.
You have one equation, then an expression. 4/x - 9/y + 1 has no equal sign.
2/x + 3/y = 2 is a hyperbola.
(3x + 2y)/xy = 2
3x - 2xy + 2y = 0
-----------
The solution I got was x=2, y=3. But I don't know what to do when getting x and y intercept since there's undefined. (like 3/0 and 9/0)

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, your second "equation" is not an equation at all. There is no "=". So I cannot tell if (2, 3) is actually the solution.

You are correct that there are no intercepts for these equations. But that does not mean there is no graph. It just means that the graph never intercepts either the x or the y axis.

If you want to graph these equations you have two choices:
  • Build a table of values by choosing values for x (or y) and then using the equation to figure out what the other variable must be. The graph is not simple so it may take a fairly large number of points to see how the graph looks.
  • Solve the equation for y and then use a graphing calculator:
    2%2Fx%2B3%2Fy=2
    xy%282%2Fx%2B3%2Fy%29=xy%282%29
    2y%2B3x=2xy
    3x=2xy-2y
    3x=y%282x-2%29
    %283x%29%2F%282x-2%29=%28y%282x-2%29%29%2F%282x-2%29
    3x%2F%282x-2%29=y
    When you look at the graph of this equation, note that the first thing we did was to multiply each side by xy. So if x or y is zero , then xy is zero, too. And multiplying both sides of an equation by zero is not something we should do. So on the graph, disregard any points where x = 0 (on the y-axis) or y = 0 (on the x-axis). (The graph should look like it passes through the origin. Disregard this point. The proper graph for your original equation will have a "hole" there.)