document.write( "Question 72621This question is from textbook Introductory and intermediate algebra
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Solve this system of equations. \r\n" );
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document.write( "       3y -  z = -1\r\n" );
document.write( "   x + 5y -  z = -4\r\n" );
document.write( " -3x + 6y + 2z = 11

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Algebra.Com's Answer #51929 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
Solve this system of equations. \r\n" );
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document.write( "       3y -  z = -1\r\n" );
document.write( "   x + 5y -  z = -4\r\n" );
document.write( " -3x + 6y + 2z = 11\r\n" );
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document.write( "Since x has already been eliminated from the 1st\r\n" );
document.write( "equation, to make things easier, we will eliminate\r\n" );
document.write( "x also from the other two equations.  To make the\r\n" );
document.write( "x's cancel we multiply the 2nd equation through \r\n" );
document.write( "by 3 and add it to the 3rd equation:\r\n" );
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document.write( "3[  x +  5y -  z = -4]\r\n" );
document.write( "1[-3x +  6y + 2z = 11]\r\n" );
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document.write( "   3x + 15y - 3z = -12\r\n" );
document.write( "  -3x +  6y + 2z =  11\r\n" );
document.write( " ----------------------\r\n" );
document.write( "        21y -  z =  -1\r\n" );
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document.write( "Now we have this system of just two equations in \r\n" );
document.write( "just two unknowns:\r\n" );
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document.write( "         3y -  z = -1\r\n" );
document.write( "        21y -  z = -1\r\n" );
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document.write( "We can eliminate z by multiplying the 1st eq.\r\n" );
document.write( "by -1 and adding to the 2nd:\r\n" );
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document.write( "     -1[ 3y -  z = -1]\r\n" );
document.write( "      1[21y -  z = -1]\r\n" );
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document.write( "        -3y +  z =  1\r\n" );
document.write( "        21y -  z = -1\r\n" );
document.write( "       ---------------\r\n" );
document.write( "        18y      =  0\r\n" );
document.write( "               y = 0\r\n" );
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document.write( "Substitute y = 0 in  \r\n" );
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document.write( "          3y - z = -1\r\n" );
document.write( "        3(0) - z = -1\r\n" );
document.write( "              -z = -1\r\n" );
document.write( "               z = 1\r\n" );
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document.write( "Finally substitute y = 0 and z = 1 into\r\n" );
document.write( "one of the original equations which \r\n" );
document.write( "contains x, say,\r\n" );
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document.write( "    x + 5y - z = -4\r\n" );
document.write( "  x + 5(0) - 1 = -4\r\n" );
document.write( "         x - 1 = -4\r\n" );
document.write( "             x = -3\r\n" );
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document.write( "So the solution is (x, y, z) = (-3, 0 1) \r\n" );
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document.write( "Edwin
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