document.write( "Question 639177: Solve.
\n" ); document.write( "2x - 3y + z = 5
\n" ); document.write( "x + 3y + 8z = 22
\n" ); document.write( "3x - y + 2z = 12\r
\n" ); document.write( "\n" ); document.write( "I've tried it by: Multiplying the second equation by 2 and the third equation by 2; as well as multiplying the second equation by 4 and the third equation by 2 but neither seemed to work. Please help. \n" ); document.write( "
Algebra.Com's Answer #402620 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(1)   2x - 3y +  z =  5\r\n" );
document.write( "(2)    x + 3y + 8z = 22\r\n" );
document.write( "(3)   3x -  y + 2z = 12\r\n" );
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document.write( "The smart thing to notice is that if you add (1) and (2)\r\n" );
document.write( "the -3y and the +3y will eliminate the y's\r\n" );
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document.write( "(1)   2x - 3y +  z =  5\r\n" );
document.write( "(2)    x + 3y + 8z = 22\r\n" );
document.write( "-----------------------\r\n" );
document.write( "      3x      + 9z = 27\r\n" );
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document.write( "and that can be divided through by 3\r\n" );
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document.write( "(4)         x + 3z = 9\r\n" );
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document.write( "Now we need another equation that does not contain y.\r\n" );
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document.write( "We multiply (3) by 3 and add it to (2)\r\n" );
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document.write( "(3)   3x -  y + 2z = 12\r\n" );
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document.write( "Multiply it by 3:\r\n" );
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document.write( "      9x - 3y + 6z = 36\r\n" );
document.write( "(2)    x + 3y + 8z = 22\r\n" );
document.write( "-----------------------\r\n" );
document.write( "     10x      +14z = 58\r\n" );
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document.write( "We can divide that through by 2 and get\r\n" );
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document.write( "(5)        5x + 7z = 29\r\n" );
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document.write( "Now we put (4) and (5) together and we now\r\n" );
document.write( "have a system of only 2 equations in only\r\n" );
document.write( "2 unknowns.\r\n" );
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document.write( "(4)         x + 3z =  9\r\n" );
document.write( "(5)        5x + 7z = 29\r\n" );
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document.write( "Multiply (4) through by -5 and add to (5)\r\n" );
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document.write( "         -5x - 15z = -45\r\n" );
document.write( "(5)       5x +  7z =  29\r\n" );
document.write( "-------------------------\r\n" );
document.write( "               -8z = -16\r\n" );
document.write( "(6)              z = 2\r\n" );
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document.write( "Substitute z = 2 into (4)\r\n" );
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document.write( "(4)         x + 3z = 9\r\n" );
document.write( "          x + 3(2) = 9\r\n" );
document.write( "             x + 6 = 9\r\n" );
document.write( "(7)              x = 3\r\n" );
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document.write( "Substitute x=3 and z=2 into (3)\r\n" );
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document.write( "(3)   3x -  y + 2z = 12\r\n" );
document.write( "    3(3)- y + 2(2) = 12\r\n" );
document.write( "         9 - y + 4 = 12\r\n" );
document.write( "            13 - y = 12\r\n" );
document.write( "                -y = -1\r\n" );
document.write( "(8)              y = 1\r\n" );
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document.write( "From (7), (8), and (6),\r\n" );
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document.write( "Solution = (x,y,z) = (3,1,2)\r\n" );
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document.write( "Edwin

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