document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=56346>Question 56346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thanks for your help!!!!!!<BR>\n" );
document.write( "Solve the systems by graphing.<BR>\n" );
document.write( "McGraw Hill 6th edtion. 8.1 # 12\r<BR>\n" );
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document.write( "x-2y=8<BR>\n" );
document.write( "3x-2y=12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #38231 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=38231\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "Problems like this are called simultaneous equations. There are quite a few techniques to solving them. The one I prefer is eliminating one variable by adding.\r<BR>\n" );
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document.write( "What we want to do is change one (or both) of the equations so that we can add them together and cancel one varibale.\r<BR>\n" );
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document.write( "In this case we have\r<BR>\n" );
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document.write( "x - 2y = 8\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "3x - 2y = 12\r<BR>\n" );
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document.write( "Let's multiply the first equation by -1. (remember that equations still hold as long as we do the same thing to both sides). We get\r<BR>\n" );
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document.write( "-x + 2y = -8\r<BR>\n" );
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document.write( "If we now add this with the second equation, we get\r<BR>\n" );
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document.write( "(3x - 2y) + (-x + 2y) = 12 + -8\r<BR>\n" );
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document.write( "Notice how we have +2y and -2y so all the terms with y have cancelled. We actually have\r<BR>\n" );
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document.write( "2x = 4\r<BR>\n" );
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document.write( "So x=2\r<BR>\n" );
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document.write( "Putting this back into either equation lets us calculate y. Try for yourself, you should get y=-3\r<BR>\n" );
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document.write( "Hope that helps,\r<BR>\n" );
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document.write( "Kev </SPAN>\n" );
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