document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2811>Question 2811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the syatem of eqations for x and y using the addition method:\r<BR>\n" );
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document.write( "2x-5y=13<BR>\n" );
document.write( "5x+3y=17 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #1202 by </B><A HREF=/tutors/aboutme.mpl?userid=sujatha.krishna><B>sujatha.krishna(11)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sujatha.krishna><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=1202\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we directly add the 2 LHS (left hand sides) and 2 RHS (right hand sides) of these equations as suggested by addition method of solving a system of linear equations, then we cannot arrive at an answer. Why ? Take a look - \r<BR>\n" );
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document.write( "2x  - 5y = 13<BR>\n" );
document.write( "5x + 3y = 17<BR>\n" );
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document.write( "7x - 2y  = 30<BR>\n" );
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document.write( "You still have two unknowns x and y. So the other way to solve this is to multiply the first equation by 3 and the second one by 5 so that we can arrive at a -15y and a +15y and hence y can be eliminated thereby giving the value of x. How does this work, take a look below -\r<BR>\n" );
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document.write( "2x - 5y = 13 (multiply this by 3) This gives 6x - 15y = 39<BR>\n" );
document.write( "5x +3y = 17 (multiply this by 5) This gives 25x + 15y = 85\r<BR>\n" );
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document.write( "6x  - 15y = 39<BR>\n" );
document.write( "25x + 15y = 85<BR>\n" );
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document.write( "31x =  124<BR>\n" );
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document.write( "So x = 124/31 = 4\r<BR>\n" );
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document.write( "Now to find the value of y, substitue the value of x in any of the equations. Lets use the first one -\r<BR>\n" );
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document.write( "2x - 5y = 13<BR>\n" );
document.write( "2(4) - 5y = 13<BR>\n" );
document.write( "-5y = 13-8 = 5<BR>\n" );
document.write( "5y = -5<BR>\n" );
document.write( "y = -5/5 = -1\r<BR>\n" );
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document.write( "So the system of these 2 equations is (4,-1)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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