document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29972>Question 29972</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me find the real solutions if any for this system?\r<BR>\n" );
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document.write( "1/x-1/y=1/4<BR>\n" );
document.write( "xy=8\r<BR>\n" );
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document.write( "i tried solving for x in the second equation which i got x=8/y and plugging in the value for x in the first equation but i get stuck there. i get 1/x/8/y-1/y=1/4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16743 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=16743\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = 8/y so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2Fx%29+-+%281%2Fy%29+=+%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+%281%2Fx%29+-+%281%2Fy%29+=+%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28y%2F8%29+-+%281%2Fy%29+=+%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+%28y%2F8%29+-+%281%2Fy%29+=+%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now multiply every term by 8y, to give<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+-+8+=+2y+ ALIGN=MIDDLE  ALT=\"+y%5E2+-+8+=+2y+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5E2+-+2y+-+8+=+0+ ALIGN=MIDDLE  ALT=\"+y%5E2+-+2y+-+8+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(y-4)(y+2) = 0\r<BR>\n" );
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document.write( "so y-4 = 0 or y+2 = 0<BR>\n" );
document.write( "--> y=4 or y = -2\r<BR>\n" );
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document.write( "When y=4, so x=8/4 --> x=2<BR>\n" );
document.write( "When y=-2, so x=8/-2 --> x=-4\r<BR>\n" );
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document.write( "CHECK:<BR>\n" );
document.write( "1. for (2,4): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2Fx%29+-+%281%2Fy%29+ ALIGN=MIDDLE  ALT=\"+%281%2Fx%29+-+%281%2Fy%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29+-+%281%2F4%29+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29+-+%281%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> 1/4... correct\r<BR>\n" );
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document.write( "2. for (-4,-2): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2Fx%29+-+%281%2Fy%29+ ALIGN=MIDDLE  ALT=\"+%281%2Fx%29+-+%281%2Fy%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F-4%29+-+%281%2F-2%29+ ALIGN=MIDDLE  ALT=\"+%281%2F-4%29+-+%281%2F-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=+%28-1%2F4%29+%2B+%281%2F2%29+ ALIGN=MIDDLE  ALT=\"+%28-1%2F4%29+%2B+%281%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--> 1/4... correct\r<BR>\n" );
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document.write( "jon.<BR>\n" );
document.write( " </SPAN>\n" );
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