document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197003>Question 197003</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321373871/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 1.Solve by substitution or elimination method: \r<BR>\n" );
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document.write( " 3x – 2y = 26<BR>\n" );
document.write( " -7x + 3y = -49\r<BR>\n" );
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document.write( "2.Solve by substitution or elimination method: <BR>\n" );
document.write( " 4x – 5y = 14<BR>\n" );
document.write( "-12x + 15y = -42\r<BR>\n" );
document.write( "\n" );
document.write( "3.Solve by substitution or elimination method: \r<BR>\n" );
document.write( "\n" );
document.write( " -2x + 6y = 1<BR>\n" );
document.write( " 10x – 30y = -15<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147950 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20055)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=147950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font size = 4 color = \"indigo\"><b>\r\n" );
document.write( "1. Solve by substitution or elimination method: \r\n" );
document.write( " 3x – 2y =  26\r\n" );
document.write( "-7x + 3y = -49 \r\n" );
document.write( "\r\n" );
document.write( "Eliminate x:\r\n" );
document.write( "\r\n" );
document.write( " 3x – 2y =  26\r\n" );
document.write( "-7x + 3y = -49 \r\n" );
document.write( "\r\n" );
document.write( "the coefficients of x are 3 and -7.\r\n" );
document.write( "Ignoring signs temporarily they are 3 and 7.\r\n" );
document.write( "The least common multiple of 3 and 7 is 21.\r\n" );
document.write( "If we multiply the first equation through by 7,\r\n" );
document.write( "there will be a 21x where the 3x is now.  If we\r\n" );
document.write( "multiply the second equation by 3, there will be\r\n" );
document.write( "a -21x where the -7x is.  And 21x and -21x will\r\n" );
document.write( "cancel out when we add equals to equals.  So \r\n" );
document.write( "let's multiply the first equation through by 7 \r\n" );
document.write( "and the second equation through by 3:\r\n" );
document.write( "\r\n" );
document.write( "7[ 3x –  2y =  26]\r\n" );
document.write( "3[-7x +  3y = -49]\r\n" );
document.write( "\r\n" );
document.write( "  21x - 14y =  182\r\n" );
document.write( " -21x +  9y = -147\r\n" );
document.write( "\r\n" );
document.write( "Draw a line underneath and add equals to equals\r\n" );
document.write( "vertically:\r\n" );
document.write( "\r\n" );
document.write( "  21x - 14y =  182\r\n" );
document.write( " -21x +  9y = -147\r\n" );
document.write( "-------------------\r\n" );
document.write( "   0x -  5y =   35    \r\n" );
document.write( "        -5y =   35\r\n" );
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document.write( "Divide both sides by -5\r\n" );
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document.write( "          y =   -7\r\n" );
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document.write( "Eliminate y:\r\n" );
document.write( "\r\n" );
document.write( " 3x – 2y =  26\r\n" );
document.write( "-7x + 3y = -49 \r\n" );
document.write( "the coefficients of y are -2 and 3.\r\n" );
document.write( "Ignoring signs temporarily they are 2 and 3.\r\n" );
document.write( "The least common multiple of 2 and 3 is 6.\r\n" );
document.write( "If we multiply the first equation through by 3,\r\n" );
document.write( "there will be a -6y where the -2y is now.  If we\r\n" );
document.write( "multiply the second equation by 2, there will be\r\n" );
document.write( "a 6y where the 3y is.  And -6y and 6y will\r\n" );
document.write( "cancel out when we add equals to equals.  So \r\n" );
document.write( "let's multiply the first equation through by 3 \r\n" );
document.write( "and the second equation through by 2:\r\n" );
document.write( "\r\n" );
document.write( "3[ 3x – 2y =  26]\r\n" );
document.write( "2[-7x + 3y = -49]\r\n" );
document.write( "\r\n" );
document.write( "   9x - 6y =  78\r\n" );
document.write( " -14x + 6y = -98 \r\n" );
document.write( "\r\n" );
document.write( "Draw a line underneath and add equals to equals\r\n" );
document.write( "vertically:\r\n" );
document.write( "\r\n" );
document.write( "   9x - 6y =  78\r\n" );
document.write( " -14x + 6y = -98 \r\n" );
document.write( "-------------------\r\n" );
document.write( "  -5x + 0y = -20     \r\n" );
document.write( "       -5x = -20 \r\n" );
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document.write( "Divide both sides by -5\r\n" );
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document.write( "          x = 4 \r\n" );
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document.write( "So the solution is \r\n" );
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document.write( "(x,y) = (4,-7)\r\n" );
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document.write( "\r\n" );
document.write( "====================================\r\n" );
document.write( "\r\n" );
document.write( "2. Solve by substitution or elimination method: \r\n" );
document.write( "\r\n" );
document.write( "  4x –  5y =  14\r\n" );
document.write( "-12x + 15y = -42 \r\n" );
document.write( "\r\n" );
document.write( "Eliminate x:\r\n" );
document.write( "\r\n" );
document.write( "  4x –  5y =  14\r\n" );
document.write( "-12x + 15y = -42\r\n" );
document.write( "\r\n" );
document.write( "The coefficients of x are 4 and -12 \r\n" );
document.write( "\r\n" );
document.write( "Ignoring signs temporarily they are 4 and 12.\r\n" );
document.write( "The least common multiple of 4 and 12 is 12.\r\n" );
document.write( "If we multiply the first equation through by 3,\r\n" );
document.write( "there will be a 12x where the 4x is now.  We don't\r\n" );
document.write( "need to do anything to the second equation for\r\n" );
document.write( "the 12x and the -12x will cancel out when we add \r\n" );
document.write( "equals to equals.  So let's multiply the first \r\n" );
document.write( "equation through by 7 and leave the second equation \r\n" );
document.write( "as it is:\r\n" );
document.write( "\r\n" );
document.write( "3[  4x –  5y =  14]\r\n" );
document.write( "  -12x + 15y = -42\r\n" );
document.write( "\r\n" );
document.write( "  12x - 15y =   42\r\n" );
document.write( " -12x + 15y =  -42\r\n" );
document.write( "\r\n" );
document.write( "Draw a line underneath and add equals to equals\r\n" );
document.write( "vertically:\r\n" );
document.write( "\r\n" );
document.write( "  12x - 15y =   42\r\n" );
document.write( " -12x + 15y =  -42\r\n" );
document.write( "-------------------\r\n" );
document.write( "   0x +  0y =   0    \r\n" );
document.write( "\r\n" );
document.write( "As you can see, any number may be substituted\r\n" );
document.write( "for x and y and that will always be true, since\r\n" );
document.write( "you'll always get 0 on the left and that will\r\n" );
document.write( "always give 0 and 0 will always equal to 0.\r\n" );
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document.write( "So there are infinitely many solutions.  This\r\n" );
document.write( "sort of system is called \"dependent\".\r\n" );
document.write( "\r\n" );
document.write( "We need go no further.  We just state that\r\n" );
document.write( "the system is dependent and has INFINITELY\r\n" );
document.write( "MANY solutions.  \r\n" );
document.write( "\r\n" );
document.write( "===============================================\r\n" );
document.write( "\r\n" );
document.write( "3. Solve by substitution or elimination method: \r\n" );
document.write( "\r\n" );
document.write( " -2x +  6y =   1\r\n" );
document.write( " 10x – 30y = -15\r\n" );
document.write( "\r\n" );
document.write( "Eliminate x:\r\n" );
document.write( "\r\n" );
document.write( " -2x +  6y =   1\r\n" );
document.write( " 10x – 30y = -15\r\n" );
document.write( "\r\n" );
document.write( "The coefficients of x are -2 and -10 \r\n" );
document.write( "\r\n" );
document.write( "Ignoring signs temporarily they are 2 and 10.\r\n" );
document.write( "The least common multiple of 2 and 10 is 10.\r\n" );
document.write( "If we multiply the first equation through by 5,\r\n" );
document.write( "there will be a -10x where the -2x is now.  We don't\r\n" );
document.write( "need to do anything to the second equation for\r\n" );
document.write( "the 10x and the -10x will cancel out when we add \r\n" );
document.write( "equals to equals.  So let's multiply the first \r\n" );
document.write( "equation through by 5 and leave the second equation \r\n" );
document.write( "as it is:\r\n" );
document.write( "\r\n" );
document.write( "5[ -2x +  6y =   1]\r\n" );
document.write( "   10x - 30y = -15\r\n" );
document.write( "\r\n" );
document.write( "  -10x + 30y =   5\r\n" );
document.write( "   10x - 30y = -15\r\n" );
document.write( "\r\n" );
document.write( "Draw a line underneath and add equals to equals\r\n" );
document.write( "vertically:\r\n" );
document.write( "\r\n" );
document.write( "  -10x + 30y =   5\r\n" );
document.write( "   10x - 30y = -15\r\n" );
document.write( "-------------------\r\n" );
document.write( "   0x +  0y =  -10    \r\n" );
document.write( "\r\n" );
document.write( "As you can see, NO number when substituted\r\n" );
document.write( "for x and y will ever be a solution, since\r\n" );
document.write( "we'll always get 0 on the left and that will\r\n" );
document.write( "NEVER equal to the -10 on the right.\r\n" );
document.write( "\r\n" );
document.write( "So there are NO solutions.  This\r\n" );
document.write( "sort of system is called \"inconsistent\".\r\n" );
document.write( "\r\n" );
document.write( "We need go no further.  We just state that\r\n" );
document.write( "the system is inconsistent and has NO\r\n" );
document.write( "solutions.\r\n" );
document.write( "\r\n" );
document.write( "Edwin</PRE> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );