document.write( "Question 542051: Solve the following 3 variable equation by using the elimination method.\r
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Algebra.Com's Answer #354423 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(1)    x  +  y -  z =  3\r\n" );
document.write( "(2)    x  - 3y + 2z = -2\r\n" );
document.write( "(3)   3x  +  y - 3z = -1\r\n" );
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document.write( "1. Pick 2 equations and a letter to eliminate from them\r\n" );
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document.write( "I will pick (1) and (2) and the letter y to eliminate from them.\r\n" );
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document.write( "(1)    x  +  y -  z =  3\r\n" );
document.write( "(2)    x  - 3y + 2z = -2\r\n" );
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document.write( "I will multiply (1) by 3 to make the term +y into +3y so it will\r\n" );
document.write( "cancel with the -3y in (2) whe we add them term by term vertically:\r\n" );
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document.write( "      3x + 3y - 3z =  9\r\n" );
document.write( "(2)    x - 3y + 2z = -2\r\n" );
document.write( "(4)   4x      -  z =  7\r\n" );
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document.write( "2. Pick a different pair of equations and eliminate the same letter\r\n" );
document.write( "   from them that you elimenated before.\r\n" );
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document.write( "I will pick (1) and (3) this time and eliminate y from them:\r\n" );
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document.write( "(1)    x  +  y -  z =  3\r\n" );
document.write( "(3)   3x  +  y - 3z = -1\r\n" );
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document.write( "I will multiply (1) by -1 to make the term +y into -y so it will\r\n" );
document.write( "cancel with the -y in (3) whe we add them term by term vertically\r\n" );
document.write( "   \r\n" );
document.write( "      -x  -  y +  z = -3\r\n" );
document.write( "(3)   3x  +  y - 3z = -1\r\n" );
document.write( "(5)   2x       - 2z = -4 \r\n" );
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document.write( "Now take (4) and (5) together:\r\n" );
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document.write( "(4)   4x -  z =  7\r\n" );
document.write( "(5)   2x - 2z = -4\r\n" );
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document.write( "I will multiply (5) by -2 to make the term 2x into -4x so it will\r\n" );
document.write( "cancel with the 4x in (4) when we add them term by term vertically\r\n" );
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document.write( "(4)   4x -  z =  7\r\n" );
document.write( "     -4x + 4z =  8\r\n" );
document.write( "           3z = 15\r\n" );
document.write( "            z = 5\r\n" );
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document.write( "Substitute 5 for z in (4)\r\n" );
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document.write( "      4x - (5) =  7\r\n" );
document.write( "      4x       = 12\r\n" );
document.write( "       x       =  3\r\n" );
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document.write( "Substitute 3 for x and 5 for z in (1):\r\n" );
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document.write( "(1)    x  +  y - z = 3\r\n" );
document.write( "       3  +  y - 5 = 3\r\n" );
document.write( "             y - 2 = 3\r\n" );
document.write( "                 y = 5\r\n" );
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document.write( "Solution (x,y,z) = (3,5,5)\r\n" );
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document.write( "Edwin
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