document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=815483>Question 815483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #490999 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=490999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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><BR>\n" );
document.write( "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><BR>\n" );
document.write( "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:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fx%2B3%2Fy=2 ALIGN=MIDDLE  ALT=\"2%2Fx%2B3%2Fy=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%282%2Fx%2B3%2Fy%29=xy%282%29 ALIGN=MIDDLE  ALT=\"xy%282%2Fx%2B3%2Fy%29=xy%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2B3x=2xy ALIGN=MIDDLE  ALT=\"2y%2B3x=2xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=2xy-2y ALIGN=MIDDLE  ALT=\"3x=2xy-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=y%282x-2%29 ALIGN=MIDDLE  ALT=\"3x=y%282x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%2F%282x-2%29=%28y%282x-2%29%29%2F%282x-2%29 ALIGN=MIDDLE  ALT=\"%283x%29%2F%282x-2%29=%28y%282x-2%29%29%2F%282x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2F%282x-2%29=y ALIGN=MIDDLE  ALT=\"3x%2F%282x-2%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "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> </SPAN>\n" );
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