document.write( "Question 242226: Please help me solve this problem Solve by Addition method x-y+z=4
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\n" ); document.write( " x+3y+2z=2 \n" ); document.write( "
Algebra.Com's Answer #178552 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " x -  y +  z =  4\r\n" );
document.write( "2x +  y - 3z = -5\r\n" );
document.write( " x + 3y + 2z =  2\r\n" );
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document.write( "Choose a letter to eliminate, and\r\n" );
document.write( "choose two of the equations that contain\r\n" );
document.write( "that letter to eliminate it from.\r\n" );
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document.write( "I choose to eliminate y from the first two\r\n" );
document.write( "equations since all I have to do is add\r\n" );
document.write( "the equations as they are and the y's\r\n" );
document.write( "will cancel out\r\n" );
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document.write( " x -  y +  z =  4\r\n" );
document.write( "2x +  y - 3z = -5\r\n" );
document.write( "-----------------\r\n" );
document.write( "3x      - 2z = -1\r\n" );
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document.write( "Choose the equation you haven't chosen yet,\r\n" );
document.write( "and another one that you have already used,\r\n" );
document.write( "to eliminate the SAME letter you eliminated\r\n" );
document.write( "before.\r\n" );
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document.write( "I haven't used the 3rd one, so I will choose\r\n" );
document.write( "it and the first one to eliminate the SAME\r\n" );
document.write( "letter I eliminated before, which is y:\r\n" );
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document.write( " x -  y +  z =  4\r\n" );
document.write( " x + 3y + 2z =  2\r\n" );
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document.write( "To eliminate y we must first multiply the\r\n" );
document.write( "first equation by 3:\r\n" );
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document.write( "3x - 3y + 3z = 12\r\n" );
document.write( " x + 3y + 2z =  2\r\n" );
document.write( "-----------------\r\n" );
document.write( "4x      + 5z = 14\r\n" );
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document.write( "So we take the two equations with y eliminated\r\n" );
document.write( "and solve them:\r\n" );
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document.write( "3x  - 2z = -1\r\n" );
document.write( "4x  + 5z = 14\r\n" );
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document.write( "Now we eliminate z by multiplying the first by 5\r\n" );
document.write( "and the second by 2\r\n" );
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document.write( "15x  - 10z = -5\r\n" );
document.write( " 8x  + 10z = 28\r\n" );
document.write( "---------------\r\n" );
document.write( "23x        = 23\r\n" );
document.write( "   \r\n" );
document.write( "       23x = 23\r\n" );
document.write( "         x = 1\r\n" );
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document.write( "Substitute 1 for x in\r\n" );
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document.write( " 3x  - 2z = -1\r\n" );
document.write( "3(1) - 2z = -1\r\n" );
document.write( "   3 - 2z = -1\r\n" );
document.write( "      -2z = -4\r\n" );
document.write( "        z = 2\r\n" );
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document.write( "Substitute x = 1 and z = 2 into\r\n" );
document.write( "one of the original equations,\r\n" );
document.write( "say the first:\r\n" );
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document.write( " x -  y + z =  4\r\n" );
document.write( " 1 -  y + 2 =  4\r\n" );
document.write( "     -y + 3 =  4 \r\n" );
document.write( "         -y =  1\r\n" );
document.write( "          y = -1\r\n" );
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document.write( "Solution: (x, y, z) = (1, -1, 2)\r\n" );
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document.write( "Edwin
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