document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=538167>Question 538167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help working this problem out.  I have no idea what I am doing.<BR>\n" );
document.write( "4a + 2b - 6c = 2<BR>\n" );
document.write( "6a + 3b - 9c = 3<BR>\n" );
document.write( "8a + 4b - 12c = 6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354780 by </B><A HREF=/tutors/aboutme.mpl?userid=jpg7n16><B>jpg7n16(66)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jpg7n16><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=354780\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The idea behind a more complicated problem like this is to make things as easy as possible. For instance, start reducing everything. Equation 1 is all multiples of 2. #2 is multiples of 3. And #3 is multiples of 4 (except the 6) - but it's worth reducing anyways.<BR>\n" );
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document.write( "The ultimate goal is to eliminate one/two of the variables to solve for the rest.<BR>\n" );
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document.write( "Step 1: reduce all the coefficients down by dividing by 2, 3 and 4 respectively<BR>\n" );
document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb-3c=1 ALIGN=MIDDLE  ALT=\"2a%2Bb-3c=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=2a%2Bb-3c=1 ALIGN=MIDDLE  ALT=\"2a%2Bb-3c=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb-3c=3%2F2 ALIGN=MIDDLE  ALT=\"2a%2Bb-3c=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And something's wrong with this problem. 2 equations are NEVER supposed to be identical after reducing. And you'll notice #1 and #2 are equal. (So one of them is irrelevant) <BR>\n" );
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document.write( "But worse than that, we know that if a=b and a=c then b=c, right? Well according to your problem:<BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb-3c=1 ALIGN=MIDDLE  ALT=\"2a%2Bb-3c=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb-3c=3%2F2 ALIGN=MIDDLE  ALT=\"2a%2Bb-3c=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=3%2F2 ALIGN=MIDDLE  ALT=\"1=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - which is def not true.<BR>\n" );
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document.write( "So there you have it. There's something wrong with the problem! It's not your fault :-) </SPAN>\n" );
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