document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82903>Question 82903</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My teacher doesn't explain well & I don't understand how to do elimination & substitution problems.<BR>\n" );
document.write( "ex.-3x-1/2y=10<BR>\n" );
document.write( "    5x+1/4y=8<BR>\n" );
document.write( "How do I figure out this problem?<BR>\n" );
document.write( "Thank you so much for your help!\r<BR>\n" );
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document.write( "Chapter 8.4 Algebra 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59493 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=59493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> how to do elimination & substitution problems.<BR>\n" );
document.write( "ex.<BR>\n" );
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document.write( "Use brackets to ensure that you mean y is not part of the denominator;<BR>\n" );
document.write( "-3x - (1/2)y = 10<BR>\n" );
document.write( " 5x + (1/4)y = 8<BR>\n" );
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document.write( "Get rid of the fractions, mult the 1st equation by 2, and the 2nd equation by 4<BR>\n" );
document.write( "Resulting in:<BR>\n" );
document.write( "-6x - 1y = 20<BR>\n" );
document.write( "20x + 1y = 32<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Notice in this problem, if we just add these two equations we eliminate y:<BR>\n" );
document.write( "-6x - y = 20<BR>\n" );
document.write( "20x + y = 32<BR>\n" );
document.write( "--------------- adding eliminates y, easy to solve for x<BR>\n" );
document.write( "14x + 0 = 52<BR>\n" );
document.write( "14x = 52<BR>\n" );
document.write( "x = 52/14; divide both sides by 14<BR>\n" );
document.write( "x = 26/7; lowest terms<BR>\n" );
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document.write( "Pick one of the equations, substitute 3 for x and solve for y:<BR>\n" );
document.write( "20x + y = 32<BR>\n" );
document.write( "20(26/7) + y = 32<BR>\n" );
document.write( "(520/7) + y = 32<BR>\n" );
document.write( "y = 32 - (520/7)<BR>\n" );
document.write( "y = (224/7) - (520/7); changed 32 to 7ths<BR>\n" );
document.write( "y = -296/7<BR>\n" );
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document.write( "Check solutions in one of the original equations:<BR>\n" );
document.write( "-3x - (1/2)y = 10<BR>\n" );
document.write( "-3(26/7) - (1/2)(-296/7) = <BR>\n" );
document.write( "(-78/7) - (-148/7) = <BR>\n" );
document.write( "(-78/7) + (148/7) =   <BR>\n" );
document.write( "+70/7 = 10; proves our solution<BR>\n" );
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document.write( "Did this help?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );