document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190535>Question 1190535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having a really hard time understanding solving using elimination. Could somebody explain it to me in lots of detail. <BR>\n" );
document.write( "x-y=3 and 2x+4y=9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822210 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=822210\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Let's multiply both sides of x-y=3 by 4<BR>\n" );
document.write( "We should end up with 4x-4y=12\r<BR>\n" );
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document.write( "The original system of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x-y=3%2C2x%2B4y=9%29 ALIGN=MIDDLE  ALT=\"system%28x-y=3%2C2x%2B4y=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is equivalent to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%284x-4y=12%2C2x%2B4y=9%29 ALIGN=MIDDLE  ALT=\"system%284x-4y=12%2C2x%2B4y=9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice how we have -4y and +4y from the first and second equations respectively. <BR>\n" );
document.write( "They add to 0y, aka 0. The y terms go away.\r<BR>\n" );
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document.write( "Let's add the terms straight down<ul><li>4x+2x becomes 6x</li><li>-4y+4y becomes 0y and goes away (hence the term \"elimination\")</li><li>12+9 becomes 21</li></ul>We're left with this equation: 6x = 21<BR>\n" );
document.write( "Divide both sides by 6 to solve for x. You should get x = 21/6 = 7/2 = 3.5\r<BR>\n" );
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document.write( "Let's plug this into any equation involving x and y, and solve for y<BR>\n" );
document.write( "x-y = 3<BR>\n" );
document.write( "3.5-y = 3<BR>\n" );
document.write( "-y = 3-3.5<BR>\n" );
document.write( "-y = -0.5<BR>\n" );
document.write( "y = 0.5<BR>\n" );
document.write( "y = 1/2\r<BR>\n" );
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document.write( "Or,<BR>\n" );
document.write( "2x+4y = 9<BR>\n" );
document.write( "2(3.5)+4y = 9<BR>\n" );
document.write( "7+4y = 9<BR>\n" );
document.write( "4y = 9-7<BR>\n" );
document.write( "4y = 2<BR>\n" );
document.write( "y = 2/4<BR>\n" );
document.write( "y = 1/2<BR>\n" );
document.write( "y = 0.5\r<BR>\n" );
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document.write( "Answer in fraction form: x = 7/2 and y = 1/2<BR>\n" );
document.write( "Answer in decimal form: x = 3.5 and y = 0.5<BR>\n" );
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