Question 815483
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.<br>
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.<br>
If you want to graph these equations you have two choices:<ul><li>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.</li> <li>Solve the equation for y and then use a graphing calculator:
{{{2/x+3/y=2}}}
{{{xy(2/x+3/y)=xy(2)}}}
{{{2y+3x=2xy}}}
{{{3x=2xy-2y}}}
{{{3x=y(2x-2)}}}
{{{(3x)/(2x-2)=(y(2x-2))/(2x-2)}}}
{{{3x/(2x-2)=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.)</li></ul>