document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242036>Question 242036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 23x/2y+6y=27 and 7x+12y/3x=22\r<BR>\n" );
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document.write( "Solve for x and y.\r<BR>\n" );
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document.write( "Can this be solved? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177195 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=177195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "This is uglier than a mud fence.\r<BR>\n" );
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document.write( "Multiply the first equation by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2y\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{23x}{2y}\ +\ 6y\ =\ 27\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 23x\ +\ 12y^2\ =\ 54y\">\r<BR>\n" );
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document.write( "Multiply the second equation by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 7x\ + \frac{12y}{3x}\ =\ 32\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 21x^2\ +\ 12y\ =\ 96x\">\r<BR>\n" );
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document.write( "Set up to solve by substitution:\r<BR>\n" );
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document.write( "Solve the first equation for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> in terms of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ \frac{-12y^2\ +\ 54y}{23}\">\r<BR>\n" );
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document.write( "Substitute this expression into the second equation in place of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 21\left(\frac{-12y^2\ +\ 54y}{23}\right)^2\ +\ 12y\ =\ 96\left(\frac{-12y^2\ +\ 54y}{23}\right)\">\r<BR>\n" );
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document.write( "You should be able to tell that this will simplify to a quartic in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> with rational coefficients.  The rational coefficients will have large integers as numerators and denominators.\r<BR>\n" );
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document.write( "Your best bet, after you have accomplished the simplification and rearranged it into standard form, would be to plug it into a graphing calculator to determine visually whether or not you actually have any real number zeros.  Since it is a quartic, you will certainly have four roots, but the possibility exists that you will have two conjugate pairs of complex numbers.\r<BR>\n" );
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document.write( "If you are happy with approximations, your graphing calculator should handle it nicely.  But if you need the exact answers, you are going to have to struggle through the general solution to a quartic.  See the following website for a discussion of that process.\r<BR>\n" );
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document.write( "http://en.wikipedia.org/wiki/Quartic_function.  Warning:  Your response when you see the website may contain strong language and may not be suitable for young children.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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