document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75567>Question 75567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by addition.<BR>\n" );
document.write( "	5x + 9y = –12<BR>\n" );
document.write( "	 x – 2y = –10<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54218 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54218\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x + 9y = –12<BR>\n" );
document.write( "+x – 2y = –10<BR>\n" );
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document.write( "To solve this pair of linear equations by addition, you need to get one of the variable terms<BR>\n" );
document.write( "in one of the equations equal but of opposite sign to the same variable term in the other<BR>\n" );
document.write( "equation.  Then you add the two equations and you end up with a new equation that contains<BR>\n" );
document.write( "only one variable.  This new equation is solvable for that single variable.  Then you <BR>\n" );
document.write( "back solve to get the other variable.<BR>\n" );
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document.write( "Let's do it. It's easier to see an example, than to explain it.<BR>\n" );
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document.write( "In these two equations, multiply the bottom equation (all terms on both sides) by -5.  This<BR>\n" );
document.write( "does not upset the balance of the bottom equation because we are multiplying both sides <BR>\n" );
document.write( "of it by the same number. When you multiply the bottom equation by -5, the resulting pair <BR>\n" );
document.write( "of equations is:<BR>\n" );
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document.write( "+5x  + 9y = –12<BR>\n" );
document.write( "-5x + 10y = +50<BR>\n" );
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document.write( "When you add the two equations vertically in columns, the +5x and the -5x cancel each other<BR>\n" );
document.write( "and what you are left with is:<BR>\n" );
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document.write( "+19y = +38<BR>\n" );
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document.write( "Divide both sides by 19 and you find that y = +2.<BR>\n" );
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document.write( "You can now take that value of y and plug it back into either of the two original <BR>\n" );
document.write( "equations and solve for x.  For example, let's take the top equation of:<BR>\n" );
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document.write( "5x + 9y = –12<BR>\n" );
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document.write( "Substitute +2 for y and the equation becomes:<BR>\n" );
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document.write( "5x + 9*2 = -12<BR>\n" );
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document.write( "Multiply out the left side:<BR>\n" );
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document.write( "5x + 18 = -12<BR>\n" );
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document.write( "Subtract 18 from both sides to get rid of the +18 on the left side.  The result is:<BR>\n" );
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document.write( "5x = -30<BR>\n" );
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document.write( "Divide both sides by 5 and the result is x = -6.  So the ordered pair representing the <BR>\n" );
document.write( "common solution to this pair of linear equations is:  (-6, +2)<BR>\n" );
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document.write( "Hope this discussion of the basic process gives you some idea of how to proceed with obtaining<BR>\n" );
document.write( "the solution.  Some times you have to multiply both equations to get two terms equal. The<BR>\n" );
document.write( "multipliers would be different for the two equations, but the goal is the same ... to <BR>\n" );
document.write( "get two terms (one in the first equation, and the other in the second equation) to be equal<BR>\n" );
document.write( "but of opposite sign so that you can add them and they cancel each other out.<BR>\n" );
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