document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572588>Question 572588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve by elimination<BR>\n" );
document.write( "6x-9y=13.5<BR>\n" );
document.write( "7y-3x=-8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368603 by </B><A HREF=/tutors/aboutme.mpl?userid=mathsmiles><B>mathsmiles(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathsmiles><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=mathsmiles><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=368603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm going to guess here on what your \"elimination\" term means, only because I hate leaving you high and dry.  \r<BR>\n" );
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document.write( "6x - 9y = 13.5  (I already hate this one btw)<BR>\n" );
document.write( "7y - 3x = -8\r<BR>\n" );
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document.write( "First thing we're going to do is line up the x's and y's since they were too lazy to do that for you:<BR>\n" );
document.write( "6x - 9y = 13.5  (unchanged)<BR>\n" );
document.write( "-3x+ 7y = -8     (reversed the first two terms)\r<BR>\n" );
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document.write( "Now if we multiply the 2nd equation (both sides) by 2, we have something interesting in the x column:<BR>\n" );
document.write( "2(-3x + 7y) = 2(-8)<BR>\n" );
document.write( "-6x + 14y = -16\r<BR>\n" );
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document.write( "Rewriting the two equations with this change:<BR>\n" );
document.write( "6x  - 9y = 13.5  (unchanged again)<BR>\n" );
document.write( "-6x + 14y = -16   <BR>\n" );
document.write( "What you'll notice is if we add these two equations vertically, the x factors cancel out so we get:\r<BR>\n" );
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document.write( "0 -9y + 14y = 13.5 - 16<BR>\n" );
document.write( "5y = -2.5   <BR>\n" );
document.write( "Divide both sides by 5<BR>\n" );
document.write( "y = -.5\r<BR>\n" );
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document.write( "But we still need x:<BR>\n" );
document.write( "6x - 9(-.5) = 13.5  Multiplying the 9 by .5 and signs cancel:<BR>\n" );
document.write( "6x + 4.5 = 13.5<BR>\n" );
document.write( "Subtract 4.5 from both sides leaving:<BR>\n" );
document.write( "6x = 9<BR>\n" );
document.write( "x = 9/6 = 3/2 = 1.5  (did they have to??  I like whole numbers myself  ;-)\r<BR>\n" );
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document.write( "Checking:<BR>\n" );
document.write( "Equation 1:<BR>\n" );
document.write( "6(1.5)-9(-.5) = 13.5<BR>\n" );
document.write( "9 + 4.5 = 13.5   (you'll want to do this step for yourself, but all I did was multiply)<BR>\n" );
document.write( "13.5 = 13.5  Correct!<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "Equation 2:<BR>\n" );
document.write( "7(-.5) - 3(1.5) = -8<BR>\n" );
document.write( "-3.5 - 4.5 = -8<BR>\n" );
document.write( "-8 = -8  Correct!\r<BR>\n" );
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document.write( "Good luck!  And please leave me feedback if I was correct in the definition of \"elimination\".  :-)<BR>\n" );
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