document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620290>Question 620290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I solve this equation using multiplication with the addition method? Also by using elimination..not substitution.<BR>\n" );
document.write( "5x - 2y = 4 <BR>\n" );
document.write( "3x + y = 9  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390069 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390069\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "Using multiplication with addition is the elimination method. Substitution is a different method.<BR>\n" );
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document.write( "Elimination Method<BR>\n" );
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document.write( "I notice that the first equation has a -2y and the second equation has a y. I'm going to MULTIPLY every term in the second equation by 2. Then I will ADD the two equations together to ELIMINATE the y-term.<BR>\n" );
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document.write( "5x - 2y = 4  ==> 5x - 2y = 4<BR>\n" );
document.write( "3x + y = 9 ===> 6x + 2y = 18<BR>\n" );
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document.write( "Add the two equations together. Notice that -2y and 2y cancel each other out because their sum is 0. Since 5x+6x=11 and 4+18=22, we have <BR>\n" );
document.write( "11x = 22 <BR>\n" );
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document.write( "Simplify.<BR>\n" );
document.write( "x=2<BR>\n" );
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document.write( "Now substitute 2 for x in either equation to find the y-value. I'll use the first.<BR>\n" );
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document.write( "5x-2y=4<BR>\n" );
document.write( "5(2)-2y=4<BR>\n" );
document.write( "10-2y=4<BR>\n" );
document.write( "-2y=-6<BR>\n" );
document.write( "y=3<BR>\n" );
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document.write( "Since x=2 and y=3, the ordered pair (2,3) in the solution to this system.<BR>\n" );
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document.write( "Remember to check this ordered pair in the original equations to make sure you didn't make a error somewhere.<BR>\n" );
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document.write( "5x - 2y = 4 <BR>\n" );
document.write( "5(2)-2(3) = 4<BR>\n" );
document.write( "10-6 = 4<BR>\n" );
document.write( "4 = 4  Check!<BR>\n" );
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document.write( "3x + y = 9 <BR>\n" );
document.write( "3(2) +(3) = 9<BR>\n" );
document.write( "6 + 3 = 9<BR>\n" );
document.write( "9 = 9 Check!<BR>\n" );
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document.write( "Hope this helps. Feel free to email if you still have questions about this.<BR>\n" );
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document.write( "Ms. Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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