document.write( "Question 554545: solve the system
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Algebra.Com's Answer #361375 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Lining the letters up vertically as below, makes it easier\r\n" );
document.write( "to see what's what:\r\n" );
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document.write( " 3x + 3y      =   3\r\n" );
document.write( "-3x      - 2z = -11\r\n" );
document.write( "       y +  z =  -1\r\n" );
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document.write( "The idea is to reduce this 3x3 system to a 2x2 system.\r\n" );
document.write( "This is done by using the three equations to obtain\r\n" );
document.write( "only two equations in only two unknowns.  \r\n" );
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document.write( "1.  We observe that x is already eliminated from the 3rd\r\n" );
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document.write( "and \r\n" );
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document.write( "2. We observe that x is easily eliminated from the 1st\r\n" );
document.write( "and 2nd equations just by adding them term by term\r\n" );
document.write( "just as they are, since the coefficients of x in them\r\n" );
document.write( "are equal in absolute value but opposite in sign.\r\n" );
document.write( "So we add them term by term:\r\n" );
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document.write( " 3x + 3y      =   3\r\n" );
document.write( "-3x      - 2z = -11\r\n" );
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document.write( "      3y - 2z =  -8\r\n" );
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document.write( "3.  Next we solve the system\r\n" );
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document.write( "3y - 2z = -8\r\n" );
document.write( " y +  z = -1\r\n" );
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document.write( "We can eliminate z if we multiply the 2nd equation (which\r\n" );
document.write( "was the 3rd original equation) by 2 and adding them term by term:\r\n" );
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document.write( "3y - 2z = -8\r\n" );
document.write( "2y + 2z = -2\r\n" );
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document.write( "5y      = -10\r\n" );
document.write( "      y = -2\r\n" );
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document.write( "4. Then we substitute -2 for y in\r\n" );
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document.write( "  y + z = -1\r\n" );
document.write( " -2 + z = -1\r\n" );
document.write( "      z = 1\r\n" );
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document.write( "5. Then finally we substitute -2 for y in\r\n" );
document.write( "the first original equation\r\n" );
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document.write( "   3x + 3y = 3\r\n" );
document.write( "3x + 3(-2) = 3\r\n" );
document.write( "    3x - 6 = 3\r\n" );
document.write( "        3x = 9\r\n" );
document.write( "         x = 3\r\n" );
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document.write( "Solution (x,y,z) = (3,-2,1)\r\n" );
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document.write( "Edwin
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