document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81744>Question 81744</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the system by addition.<BR>\n" );
document.write( "	2x – 8y = –5<BR>\n" );
document.write( "	4x + 4y = –5<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 #58566 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=58566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "2x - 8y = -5<BR>\n" );
document.write( "4x + 4y = -5<BR>\n" );
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document.write( "You can't solve this directly by addition as the problem requires because no term on the<BR>\n" );
document.write( "left side of the top equation is identical to a corresponding term in the bottom equation.<BR>\n" );
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document.write( "Notice that if we multiplied all the terms on both sides of the bottom equation by 2 we<BR>\n" );
document.write( "would get the equation set:<BR>\n" );
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document.write( "2x - 8y = -5  <---unchanged<BR>\n" );
document.write( "8x + 8y = -10  <--- all terms doubled<BR>\n" );
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document.write( "Now notice that the top equation has a y term of -8y and the bottom equation has a y term<BR>\n" );
document.write( "of +8y.  If we add the two equations vertically the -8y in the top equation cancels the<BR>\n" );
document.write( "+8y in the bottom equation and the vertical addition results in:<BR>\n" );
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document.write( "10x = - 15<BR>\n" );
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document.write( "Solve this for x by dividing both sides of this resulting equation by the multiplier of<BR>\n" );
document.write( "the x term (the multiplier is 10 so divide both sides by 10). When you do the equation<BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "x = -15/10 = -3/2<BR>\n" );
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document.write( "So now we know x. All we have to do is to return to one of the two original equations,<BR>\n" );
document.write( "substitute -3/2 for x in that equation, and solve for y.  Let's go to the top equation:<BR>\n" );
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document.write( "2x - 8y = -5<BR>\n" );
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document.write( "Substitute -3/2 for x and the equation becomes:<BR>\n" );
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document.write( "2(-3/2) - 8y = -5<BR>\n" );
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document.write( "Multiply 2 times -3/2 and you get -3.  Substitute this into the equation and it becomes<BR>\n" );
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document.write( "-3 - 8y = -5<BR>\n" );
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document.write( "Get rid of the -3 on the left side by adding 3 to both sides to cancel it.  When you do<BR>\n" );
document.write( "that the equation becomes:<BR>\n" );
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document.write( "-8y = -2<BR>\n" );
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document.write( "Solve for y by dividing both sides of the equation by -8. The equation becomes:<BR>\n" );
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document.write( "y = -2/-8 = 2/8 = 1/4<BR>\n" );
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document.write( "So the answers are x = -3/2 and y = + 1/4<BR>\n" );
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document.write( "Hope this helps you to understand the problem.<BR>\n" );
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