document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572164>Question 572164</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve this system by using the elimination method?\r<BR>\n" );
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document.write( "{2x-y=20<BR>\n" );
document.write( "{3x+2y=-19 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368607 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=368607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2x - y  = 20<BR>\n" );
document.write( "3x + 2y = -19\r<BR>\n" );
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document.write( "With the elimination method, we want to add down the columns so one of factors cancels out.  I'm going to pick y to \"eliminate\" here.  One y is already negative and the other positive.  That helps.  All I need to do then is make their multipliers the same.  So I'm going to multiply the whole first equation by 2 to give y its 2 factor.  \r<BR>\n" );
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document.write( "2x - y   =20<BR>\n" );
document.write( "2(2x - y) = 2(20)<BR>\n" );
document.write( "4x - 2y = 40\r<BR>\n" );
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document.write( "Now let's line up the equations again with this altered (but equivalent 2nd equation)\r<BR>\n" );
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document.write( "4x - 2y = 40<BR>\n" );
document.write( "3x + 2y = -19  Adding vertically (use a line under the two and add columns)<BR>\n" );
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document.write( "7x      = 21   Divide both sides by 7<BR>\n" );
document.write( " x = 3\r<BR>\n" );
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document.write( "Substituting to find y in the 1st equation:<BR>\n" );
document.write( "2(3)-y = 20<BR>\n" );
document.write( "6 - y = 20  Subtract 6 from both sides:<BR>\n" );
document.write( "-y = 14   Multiply both sides by -1<BR>\n" );
document.write( "y = -14\r<BR>\n" );
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document.write( "Checking:<BR>\n" );
document.write( "1st equation:<BR>\n" );
document.write( "2(3) - (-14) = 20<BR>\n" );
document.write( "6 + 14 = 20 Correct!\r<BR>\n" );
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document.write( "2nd equation:<BR>\n" );
document.write( "3(3) + 2(-14) = -19<BR>\n" );
document.write( "9 - 28 = -19<BR>\n" );
document.write( "-19 = -19  Correct!\r<BR>\n" );
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document.write( " </SPAN>\n" );
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