document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=106811>Question 106811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x+y+z=30000 \r<BR>\n" );
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document.write( ".02x+.03y+.06z=1110 \r<BR>\n" );
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document.write( ".02x+150=.03y : solve for x,y, and z.\r<BR>\n" );
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document.write( "The problem im having with this problem is the \"z\" variable. It is only on 2 of the 3 equations. Ive been trying to solve by using the method of elimination, but I cant seem to isolate the variables. thank you.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77732 by </B><A HREF=/tutors/aboutme.mpl?userid=HyperBrain><B>HyperBrain(694)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=HyperBrain><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=77732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Elimination method is perfect for this system!\r<BR>\n" );
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document.write( "First let's eliminate x!  To do that, let's use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=30000 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=30000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.02x%2B.03y%2B.06z=1110+ ALIGN=MIDDLE  ALT=\".02x%2B.03y%2B.06z=1110+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Let's multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2Bz=30000 ALIGN=MIDDLE  ALT=\"x%2By%2Bz=30000\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 2!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y%2B2z=60000 ALIGN=MIDDLE  ALT=\"2x%2B2y%2B2z=60000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, let's multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.02x%2B0.03y%2B0.06z=1110+ ALIGN=MIDDLE  ALT=\"0.02x%2B0.03y%2B0.06z=1110+\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 100!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y%2B6z=111000 ALIGN=MIDDLE  ALT=\"2x%2B3y%2B6z=111000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It's elimination time!\r<BR>\n" );
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document.write( "Line up the equations\r<BR>\n" );
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document.write( "_____________________________2x+3y+6z=111000<BR>\n" );
document.write( "_____________________________2x+2y+2z=60000\r<BR>\n" );
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document.write( "If you subtract <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B2y%2B2z=60000 ALIGN=MIDDLE  ALT=\"2x%2B2y%2B2z=60000\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y%2B6z=111000 ALIGN=MIDDLE  ALT=\"2x%2B3y%2B6z=111000\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "you'll get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4z=51000 ALIGN=MIDDLE  ALT=\"y%2B4z=51000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B4z=51000 ALIGN=MIDDLE  ALT=\"y%2B4z=51000\"   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=-4z%2B51000 ALIGN=MIDDLE  ALT=\"y=-4z%2B51000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, let's eliminate y! we'll do that by using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.02x%2B0.03y%2B0.06z=1110+ ALIGN=MIDDLE  ALT=\"0.02x%2B0.03y%2B0.06z=1110+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and   <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.02x%2B150=0.03y ALIGN=MIDDLE  ALT=\"0.02x%2B150=0.03y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.02x%2B150=0.03y ALIGN=MIDDLE  ALT=\"0.02x%2B150=0.03y\"   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=0.02x-0.03y=-150 ALIGN=MIDDLE  ALT=\"0.02x-0.03y=-150\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiplying this by 100,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=-15000 ALIGN=MIDDLE  ALT=\"2x-3y=-15000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.02x%2B.03y%2B.06z=1110+ ALIGN=MIDDLE  ALT=\".02x%2B.03y%2B.06z=1110+\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 100,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3y%2B6z=111000 ALIGN=MIDDLE  ALT=\"2x%2B3y%2B6z=111000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "it's elimination time!\r<BR>\n" );
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document.write( "Line up the equations!\r<BR>\n" );
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document.write( "______________________________2x+3y+6z=111000<BR>\n" );
document.write( "______________________________2x-3y   =-15000\r<BR>\n" );
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document.write( "If you add these, you'll get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%2B6z=96000 ALIGN=MIDDLE  ALT=\"4x%2B6z=96000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solving this,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=-6z%2B96000 ALIGN=MIDDLE  ALT=\"4x=-6z%2B96000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3z%2F2%2B24000 ALIGN=MIDDLE  ALT=\"x=-3z%2F2%2B24000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3z%2F2%2B24000 ALIGN=MIDDLE  ALT=\"x=-3z%2F2%2B24000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4z%2B51000 ALIGN=MIDDLE  ALT=\"y=-4z%2B51000\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=-15000 ALIGN=MIDDLE  ALT=\"2x-3y=-15000\"   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=2%28-3z%2F2%2B24000%29-3%28-4z%2B51000%29=-15000 ALIGN=MIDDLE  ALT=\"2%28-3z%2F2%2B24000%29-3%28-4z%2B51000%29=-15000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3z%2B48000-%28-12z%2B153000%29=-15000 ALIGN=MIDDLE  ALT=\"-3z%2B48000-%28-12z%2B153000%29=-15000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3z%2B48000%2B12z-153000=-15000 ALIGN=MIDDLE  ALT=\"-3z%2B48000%2B12z-153000=-15000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3z%2B12z%29%2B%2848000-153000%29=-15000 ALIGN=MIDDLE  ALT=\"%28-3z%2B12z%29%2B%2848000-153000%29=-15000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9z-105000=-15000 ALIGN=MIDDLE  ALT=\"9z-105000=-15000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9z=-15000%2B105000 ALIGN=MIDDLE  ALT=\"9z=-15000%2B105000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9z=90000 ALIGN=MIDDLE  ALT=\"9z=90000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=10000 ALIGN=MIDDLE  ALT=\"z=10000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Yahoo! we found the value of z at last!\r<BR>\n" );
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document.write( "But wait, there's more!\r<BR>\n" );
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document.write( "Remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3z%2F2%2B24000 ALIGN=MIDDLE  ALT=\"x=-3z%2F2%2B24000\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2810000%29%2F2%2B24000 ALIGN=MIDDLE  ALT=\"x=-3%2810000%29%2F2%2B24000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-30000%2F2%2B24000 ALIGN=MIDDLE  ALT=\"x=-30000%2F2%2B24000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-15000%2B24000 ALIGN=MIDDLE  ALT=\"x=-15000%2B24000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13000 ALIGN=MIDDLE  ALT=\"x=13000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4z%2B51000 ALIGN=MIDDLE  ALT=\"y=-4z%2B51000\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-4%2810000%29%2B51000 ALIGN=MIDDLE  ALT=\"y=-4%2810000%29%2B51000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-40000%2B51000=11000 ALIGN=MIDDLE  ALT=\"y=-40000%2B51000=11000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "therefore, x=13000, y=11000, and z=10000.\r<BR>\n" );
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document.write( "Power up,<BR>\n" );
document.write( "HyperBrain! </SPAN>\n" );
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