document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63610>Question 63610</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve this system of equation using the substitution and elimination methods.\r<BR>\n" );
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document.write( "8x + 9 = -5y<BR>\n" );
document.write( "-3x + 3y = -21 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44351 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</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=44351\">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><b>Can you please help me solve this system of equation \r\n" );
document.write( "using the substitution and elimination methods. \r\n" );
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document.write( " 8x + 9 = -5y\r\n" );
document.write( "-3x + 3y = -21\r\n" );
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document.write( "Rules for the substitution method:\r\n" );
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document.write( "1. Solve either equation for either letter.  Call the letter you picked\r\n" );
document.write( "   the \"first\" letter.You'll get an expression, not a numerical value, \r\n" );
document.write( "   for the first letter.  That expression will contain the other letter,\r\n" );
document.write( "   which we call the \"second\" letter.\r\n" );
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document.write( "2. Substitute the expression you get for the first letter in the OTHER \r\n" );
document.write( "   equation.\r\n" );
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document.write( "3. Solve for the value of the second letter. You'll get the actual value \r\n" );
document.write( "   for the second letter.  \r\n" );
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document.write( "4.  Substitute that value for the second letter in either equation.\r\n" );
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document.write( "5. Solve for the first letter.  You'll get the value of the first letter.  \r\n" );
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document.write( " 8x + 9 = -5y\r\n" );
document.write( "-3x + 3y = -21\r\n" );
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document.write( "1. Let's choose the bottom equation and choose the first letter as y.\r\n" );
document.write( "   We solve for y:\r\n" );
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document.write( "   -3x + 3y = -21\r\n" );
document.write( "   +3x            + 3x\r\n" );
document.write( "  -------------------\r\n" );
document.write( "         3y = -21 + 3x\r\n" );
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document.write( "Divide every term by the coefficient of y, which is 3:\r\n" );
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document.write( "       3y/3 = -21/3 + 3x/3\r\n" );
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document.write( "          y = -7 + x\r\n" );
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document.write( "2. Substitute the expression (-7 + x) for y in the top equation \r\n" );
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document.write( "     8x + 9 = -5y\r\n" );
document.write( "     8x + 9 = -5(-7 + x)\r\n" );
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document.write( "3. Solve for x\r\n" );
document.write( "     8x + 9 = 35 - 5x\r\n" );
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document.write( "     8x + 9 = 35 - 5x\r\n" );
document.write( "         -9   -9\r\n" );
document.write( "    ---------------------\r\n" );
document.write( "     8x     = 26 - 5x\r\n" );
document.write( "    +5x          + 5x  \r\n" );
document.write( "  -------------------------\r\n" );
document.write( "    13x     = 26\r\n" );
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document.write( "   Divide both sides by 13\r\n" );
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document.write( "     13x/13 = 26/13\r\n" );
document.write( "          x = 2\r\n" );
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document.write( "4.  Substitute x = 2 in either of the original\r\n" );
document.write( "    equations.  I'll arbitrarily pick the first \r\n" );
document.write( "    one:\r\n" );
document.write( "    \r\n" );
document.write( "     8x + 9 = -5y\r\n" );
document.write( "   8(2) + 9 = -5y\r\n" );
document.write( "     16 + 9 = -5y\r\n" );
document.write( "         25 = -5y\r\n" );
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document.write( "Divide both sides by -5\r\n" );
document.write( "         \r\n" );
document.write( "    25/(-5) = -5y/(-5)\r\n" );
document.write( "         -5 = y\r\n" );
document.write( "          y = -5\r\n" );
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document.write( "So now we have the solution: (x, y) = (2, -5) \r\n" );
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document.write( "Rule for the elimination method:\r\n" );
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document.write( "1. Choose a letter to eliminate, call it the \"first\" letter.\r\n" );
document.write( "2. Arrange the equations so that the corresponding terms are\r\n" );
document.write( "   lined up vertically.\r\n" );
document.write( "3. Find the LCM of the absolute values of the two coefficients\r\n" );
document.write( "   of the first letter.\r\n" );
document.write( "4. Multiply each of the two equations respectively through by \r\n" );
document.write( "   whatever pair of numbers will cause the two coefficients to \r\n" );
document.write( "   have the same absolute value but opposite in sign.\r\n" );
document.write( "5. Add term-by term vertically. You will get an equation in\r\n" );
document.write( "   only the second letter.\r\n" );
document.write( "6. Solve for the second letter.\r\n" );
document.write( "7. You have a choice here:\r\n" );
document.write( "    (a) Substitute the velue of the second letter in either \r\n" );
document.write( "        equation to find the value of the first letter\r\n" );
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document.write( "     OR\r\n" );
document.write( "    (b) Start over with step 1 but this time choose the other\r\n" );
document.write( "        letter to eliminate.\r\n" );
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document.write( " 8x + 9 = -5y\r\n" );
document.write( "-3x + 3y = -21\r\n" );
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document.write( "1.  Arbitrarily choose x to eliminate:\r\n" );
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document.write( "2.  Line up the equations vertically like this:\r\n" );
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document.write( "    8x + 5y = -9\r\n" );
document.write( "   -3x + 3y = -21\r\n" );
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document.write( "3.  The LCM of 8 and 3 is 24. \r\n" );
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document.write( "4.  Multiply the first equation through by 3 and \r\n" );
document.write( "    the second through by 8\r\n" );
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document.write( "    3[  8x + 5y = -9  ]\r\n" );
document.write( "    8[ -3x + 3y = -21 ]   \r\n" );
document.write( "  \r\n" );
document.write( "      24x + 15y =  -27\r\n" );
document.write( "     -24x + 24y = -168\r\n" );
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document.write( "5. Add term-by term vertically:\r\n" );
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document.write( "      24x + 15y =  -27\r\n" );
document.write( "     -24x + 24y = -168\r\n" );
document.write( "   -----------------------\r\n" );
document.write( "            39y = -195\r\n" );
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document.write( "6.  Solve for y: \r\n" );
document.write( "            39y = -195\r\n" );
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document.write( "    Divide both sides by 39\r\n" );
document.write( "              y = -5\r\n" );
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document.write( "7.  I'll choose to start over.\r\n" );
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document.write( " 8x + 9 = -5y\r\n" );
document.write( "-3x + 3y = -21\r\n" );
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document.write( "1.  This time I choose y to eliminate:\r\n" );
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document.write( "2.  Line up the equations vertically like this:\r\n" );
document.write( "\r\n" );
document.write( "    8x + 5y = -9\r\n" );
document.write( "   -3x + 3y = -21\r\n" );
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document.write( "3.  The LCM of 5 and 3 is 15. \r\n" );
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document.write( "4.  Multiply the first equation through by 3 and \r\n" );
document.write( "    the second through by -5\r\n" );
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document.write( "    3[  8x + 5y = -9  ]\r\n" );
document.write( "   -5[ -3x + 3y = -21 ]   \r\n" );
document.write( "  \r\n" );
document.write( "      24x + 15y = -27\r\n" );
document.write( "      15x - 15y = 105\r\n" );
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document.write( "5. Add term-by term vertically:\r\n" );
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document.write( "      24x + 15y = -27\r\n" );
document.write( "      15x - 15y = 105\r\n" );
document.write( "   -----------------------\r\n" );
document.write( "      39x       =  78\r\n" );
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document.write( "6.  Solve for x: \r\n" );
document.write( "            39x = 78\r\n" );
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document.write( "    Divide both sides by 39\r\n" );
document.write( "              y = 2\r\n" );
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document.write( "So now we have the solution: (x, y) = (2, -5)\r\n" );
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document.write( "Edwin</PRE>  </SPAN>\n" );
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