document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=15519>Question 15519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please solve the following system of equations:\r<BR>\n" );
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document.write( "x + y = -1\r<BR>\n" );
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document.write( "1/x + 1/y = 1/2\r<BR>\n" );
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document.write( "I've tried cross multiplying and all sorts to eliminate one of the unknowns, but have just made things worse.\r<BR>\n" );
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document.write( "Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7691 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=7691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the system of equations:\r<BR>\n" );
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document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+-1 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+%2B+1%2Fy+=+1%2F2 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2Fy+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify this equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+%2B+1%2Fy+=+1%2F2 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2Fy+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the fractions of the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+y%29%2Fxy+=+1%2F2 ALIGN=MIDDLE  ALT=\"%28x+%2B+y%29%2Fxy+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by xy<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+xy%2F2 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+xy%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+-1 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy%2F2+=+-1 ALIGN=MIDDLE  ALT=\"xy%2F2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+=+-2 ALIGN=MIDDLE  ALT=\"xy+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you can solve this system of two equations:\r<BR>\n" );
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document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+-1 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy+=+-2 ALIGN=MIDDLE  ALT=\"xy+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rewrite equation 1) as:<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-y-1 ALIGN=MIDDLE  ALT=\"x+=+-y-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and substitute into equation 2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-y-1%29y+=+-2 ALIGN=MIDDLE  ALT=\"%28-y-1%29y+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%5E2+-+y+=+-2 ALIGN=MIDDLE  ALT=\"-y%5E2+-+y+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 2 to both sides and simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+%2B+y+-+2+=+0 ALIGN=MIDDLE  ALT=\"y%5E2+%2B+y+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve by factoring.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y+-+1%29%28y+%2B+2%29+=+0 ALIGN=MIDDLE  ALT=\"%28y+-+1%29%28y+%2B+2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero products principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+-+1+=+0 ALIGN=MIDDLE  ALT=\"y+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"y+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+1 ALIGN=MIDDLE  ALT=\"y+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-2 ALIGN=MIDDLE  ALT=\"y+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now solve for x.\r<BR>\n" );
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document.write( "For y = 1, x = -y-1 = -1-1 = -2<BR>\n" );
document.write( "For y = -2, x = -(-2)-1 = 2 - 1 = 1\r<BR>\n" );
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document.write( "The solutions are:\r<BR>\n" );
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document.write( "1) (-2, 1)<BR>\n" );
document.write( "2) (1, -2)\r<BR>\n" );
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document.write( "Check the graph to see what this looks llike:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C+200%2C+-6%2C6%2C-6%2C6%2C-x-1%2C2x%2F%28x-2%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C+200%2C+-6%2C6%2C-6%2C6%2C-x-1%2C2x%2F%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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