document.write( "Question 1197030: Solve the given system of equations. / Los die gegwe stelsel van vergelykings op. (12)
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Algebra.Com's Answer #830145 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Solve the given system of equations. / Los die gegwe stelsel van vergelykings op. (12)
\n" ); document.write( "4x + y + 3z = 1
\n" ); document.write( "8x + 9z = 10
\n" ); document.write( "- 6x + 3y + 12z = - 4
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document.write( "    4x + y +   3z =  1      (1)\r\n" );
document.write( "    8x +       9z = 10      (2)\r\n" );
document.write( "   -6x + 3y + 12z = -4      (3)\r\n" );
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document.write( "Multiply equation (1) by 2\r\n" );
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document.write( "    8x + 2y +  6z =  2.\r\n" );
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document.write( "Replace here 8x by  (10 - 9z),  based on equation (2). You will get\r\n" );
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document.write( "    (10-9z) + 2y + 6z = 2,\r\n" );
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document.write( "or\r\n" );
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document.write( "    2y -3z = -8.        (4)\r\n" );
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document.write( "Multiply equation (3) by 4\r\n" );
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document.write( "    -24x + 12y + 48z = -16.\r\n" );
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document.write( "Replace here -24x  by  -3*(10 - 9z),  based on equation (2). You will get\r\n" );
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document.write( "    -3*(10-9z) + 12y + 48z = -16,\r\n" );
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document.write( "or\r\n" );
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document.write( "    12y + 75z = 14.     (5)\r\n" );
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document.write( "So, you reduced the original system (1),(2),(3) to two equations (4) and (5)\r\n" );
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document.write( "     2y -  3z = -8.     (4)\r\n" );
document.write( "    12y + 75z = 14.     (5)\r\n" );
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document.write( "Nultiply equation (4) by 6; keep equation (5) as is\r\n" );
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document.write( "    12y - 18z = -48.    (4)\r\n" );
document.write( "    12y + 75z =  14.    (5)\r\n" );
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document.write( "Subtract equation (4) from equation(5).  The terms with \"12y\" will casncel each other, and you will get\r\n" );
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document.write( "          93z = 62,  giving  z = 62/93 = 2/3.\r\n" );
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document.write( "Substituting z= 2/3 into equation (5), you get\r\n" );
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document.write( "    12y + 50 = 14,  giving  12y = -36,  y = -36/12 = -3.\r\n" );
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document.write( "Substituting z= 2/3 into equation (2), you get\r\n" );
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document.write( "    8x + 6 = 10,    giving  8x = 4,  x = 4/8 = 1/2.\r\n" );
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document.write( "ANSWER.  x= 1/2,  y= -3,  z= 2/3.\r\n" );
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document.write( "CHECK.  I checked this solution by substituting the found values into original equations and got confirmation.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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