document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182272>Question 182272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> BEEHIVE.... A farmer is tracking two wild honey bees in his field. He maps the first bee's path to the hive on the line 7y = 9x<BR>\n" );
document.write( "       The second bee's path follows the line y = -3x + 12. Their paths cross at the hive. At what coordinates will the farmer find the hive?\r<BR>\n" );
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document.write( "I think that I should try to line the variables up on one side, then add one set of variables together and also the integers and then solve for that respective variable.  After solving for that variable, I can plug it back into one the two line equations and then find the other variable.  The two variable points I get are where the bees' paths intersect?\r<BR>\n" );
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document.write( "I made 7y=9x----> 7y-9x=0\r<BR>\n" );
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document.write( "I made y=-3x+12----> y+3x=12\r<BR>\n" );
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document.write( "I then added the x's together and get -6x=12...solving by division for x, I get x=-2\r<BR>\n" );
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document.write( "plugging -2 for x back into the second equation I get y=18 but this does not work at all for the top equation!\r<BR>\n" );
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document.write( "Where have I gone wrong or what do I need to do differently???? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136812 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=136812\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y+=+9x ALIGN=MIDDLE  ALT=\"7y+=+9x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3x+%2B+12 ALIGN=MIDDLE  ALT=\"y+=+-3x+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the simultaneous solution like this:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y+-+9x+=+0 ALIGN=MIDDLE  ALT=\"7y+-+9x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+3x+=+12 ALIGN=MIDDLE  ALT=\"y+%2B+3x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides of (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and add the equations<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y+-+9x+=+0 ALIGN=MIDDLE  ALT=\"7y+-+9x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y+%2B+9x+=+36 ALIGN=MIDDLE  ALT=\"3y+%2B+9x+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y+=+36 ALIGN=MIDDLE  ALT=\"10y+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+18%2F5 ALIGN=MIDDLE  ALT=\"y+=+18%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now plug this result back into either (1) or (2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F5+%2B+3x+=+12 ALIGN=MIDDLE  ALT=\"18%2F5+%2B+3x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+%2B+15x+=+60 ALIGN=MIDDLE  ALT=\"18+%2B+15x+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x+=+60+-+18 ALIGN=MIDDLE  ALT=\"15x+=+60+-+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x+=+42 ALIGN=MIDDLE  ALT=\"15x+=+42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+14%2F5 ALIGN=MIDDLE  ALT=\"x+=+14%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The hive is at (14/5,18/5)<BR>\n" );
document.write( "check answers:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7y+-+9x+=+0 ALIGN=MIDDLE  ALT=\"7y+-+9x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A%2818%2F5%29+-+9%2A%2814%2F5%29+=+0 ALIGN=MIDDLE  ALT=\"7%2A%2818%2F5%29+-+9%2A%2814%2F5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126%2F5+-+126%2F5+=+0 ALIGN=MIDDLE  ALT=\"126%2F5+-+126%2F5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+0 ALIGN=MIDDLE  ALT=\"0+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+3x+=+12 ALIGN=MIDDLE  ALT=\"y+%2B+3x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F5+%2B+3%2A%2814%2F5%29+=+12 ALIGN=MIDDLE  ALT=\"18%2F5+%2B+3%2A%2814%2F5%29+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+%2B+42+=+60 ALIGN=MIDDLE  ALT=\"18+%2B+42+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60+=+60 ALIGN=MIDDLE  ALT=\"60+=+60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-6%2C+6%2C+-6%2C+6%2C-3x+%2B+12%2C+%289%2F7%29%2Ax%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-6%2C+6%2C+-6%2C+6%2C-3x+%2B+12%2C+%289%2F7%29%2Ax%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The crossing looks about right </SPAN>\n" );
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