document.write( "Question 829498: solve the system
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Algebra.Com's Answer #499903 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I corrected the error which the other tutor observed \r\n" );
document.write( "and changed the x to z.\r\n" );
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document.write( "Line them up like this:\r\n" );
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document.write( "(1)      x + 2y +  z = -3 \r\n" );
document.write( "(2)     2x - 2y +  z =  4 \r\n" );
document.write( "(3)      x -  y + 2z =  5 \r\n" );
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document.write( "We pick a letter to eliminate and then pick two of the\r\n" );
document.write( "equations to eliminate it from.\r\n" );
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document.write( "We notice that if we add (1) and (2) the y's cancel out,\r\n" );
document.write( "so we pick y to eliminate and we pick (1) and (2) to\r\n" );
document.write( "eliminate it from.  So we add (1) and (2)\r\n" );
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document.write( "(1)      x + 2y +  z = -3 \r\n" );
document.write( "(2)     2x - 2y +  z =  4  \r\n" );
document.write( "-------------------------\r\n" );
document.write( "(4)     3x      + 2z =  1\r\n" );
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document.write( "Now we pick a different pair to eliminate the same letter\r\n" );
document.write( "y from.\r\n" );
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document.write( "If we multiply (3) by 2 and add it to (1) the y's will\r\n" );
document.write( "cancel\r\n" );
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document.write( "(1)      x + 2y +  z = -3 \r\n" );
document.write( "        2x - 2y + 4z = 10\r\n" );
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document.write( "(5)     3x      + 5z =  7\r\n" );
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document.write( "So we have this system of two equations in two unknowns:\r\n" );
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document.write( "(4)     3x + 2z =  1\r\n" );
document.write( "(5)     3x + 5z =  7\r\n" );
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document.write( "If we multiply (4) by -1 and add (5) to it the x's will \r\n" );
document.write( "cancel:\r\n" );
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document.write( "       -3x - 2z = -1\r\n" );
document.write( "(5)     3x + 5z =  7\r\n" );
document.write( "--------------------\r\n" );
document.write( "             3z =  6\r\n" );
document.write( "              z =  2\r\n" );
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document.write( "Substitute z = 2 in (4)\r\n" );
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document.write( "(4)   3x + 2(2) =  1\r\n" );
document.write( "         3x + 4 =  1\r\n" );
document.write( "             3x = -3\r\n" );
document.write( "              x = -1\r\n" );
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document.write( "Substitute z = 2 and x = -1 in (1)\r\n" );
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document.write( "(1)      x + 2y +  z = -3\r\n" );
document.write( "        -1 + 2y +  2 = -3\r\n" );
document.write( "              2y + 1 = -3\r\n" );
document.write( "                  2y = -4\r\n" );
document.write( "                   y = -2\r\n" );
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document.write( "(x,y,z) = (-1,-2,2)\r\n" );
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document.write( "Edwin
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