document.write( "Question 73449This question is from textbook
\n" ); document.write( ": Please help me with this problem\r
\n" ); document.write( "\n" ); document.write( "Solve the following system of Equations
\n" ); document.write( "6x-4y+5z=31
\n" ); document.write( "5x+2y+2z=13
\n" ); document.write( "x+y+z=2 \n" ); document.write( "
Algebra.Com's Answer #52571 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "6x - 4y + 5z = 31\r\n" );
document.write( "5x + 2y + 2z = 13\r\n" );
document.write( " x +  y +  z =  2\r\n" );
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document.write( "1. Pick a letter to eliminate.\r\n" );
document.write( "2. Pick a pair of equations and \r\n" );
document.write( "   eliminate that letter\r\n" );
document.write( "3. Pick a different pair of equations\r\n" );
document.write( "   and eliminate the SAME letter you\r\n" );
document.write( "   eliminated in step 1.\r\n" );
document.write( "4. Now you have a system of two \r\n" );
document.write( "   equations in two unknowns. Solve\r\n" );
document.write( "   for the two unknowns.\r\n" );
document.write( "5. Substitute these values in one of\r\n" );
document.write( "   the original equations to find\r\n" );
document.write( "   the value of the first unknown\r\n" );
document.write( "   eliminated in step 1.\r\n" );
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document.write( "6x - 4y + 5z = 31\r\n" );
document.write( "5x + 2y + 2z = 13\r\n" );
document.write( " x +  y +  z =  2\r\n" );
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document.write( "1. Pick a letter to eliminate.\r\n" );
document.write( "\r\n" );
document.write( "   I arbitrarily pick y.\r\n" );
document.write( "\r\n" );
document.write( "2. Pick a pair of equations and \r\n" );
document.write( "   eliminate that letter\r\n" );
document.write( "\r\n" );
document.write( "   I arbitrarily pick the first\r\n" );
document.write( "   and third equations to eliminate \r\n" );
document.write( "   y.\r\n" );
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document.write( "To eliminate y I multiply the 3rd\r\n" );
document.write( "equation through by 4 to make the\r\n" );
document.write( "y-term become +4y so it will cancel\r\n" );
document.write( "out with the -4y term in the 1st\r\n" );
document.write( "equation:\r\n" );
document.write( "\r\n" );
document.write( "  6x - 4y + 5z = 31\r\n" );
document.write( "4[ x +  y +  z =  2]\r\n" );
document.write( "\r\n" );
document.write( "  6x - 4y + 3z = 31\r\n" );
document.write( "  4x + 4y + 4z =  8\r\n" );
document.write( " -------------------\r\n" );
document.write( " 10x      + 9z = 39\r\n" );
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document.write( "3. Pick a different pair of equations\r\n" );
document.write( "   and eliminate the SAME letter you\r\n" );
document.write( "   eliminated in step 1.\r\n" );
document.write( "\r\n" );
document.write( "   I arbitrarily pick the second\r\n" );
document.write( "   and third equations to eliminate \r\n" );
document.write( "   the same letter y.\r\n" );
document.write( "\r\n" );
document.write( "To eliminate y I multiply the 3rd\r\n" );
document.write( "equation through by -2 to make the\r\n" );
document.write( "y-term become -2y so it will cancel\r\n" );
document.write( "out with the +2y term in the 2nd\r\n" );
document.write( "equation:\r\n" );
document.write( "\r\n" );
document.write( "   5x + 2y + 2z = 13\r\n" );
document.write( "-2[ x +  y +  z =  2]\r\n" );
document.write( "\r\n" );
document.write( "   5x + 2y + 2z = 13\r\n" );
document.write( "  -2x - 2y - 2z = -4\r\n" );
document.write( " --------------------\r\n" );
document.write( "   3x           =  9\r\n" );
document.write( "              x = 3 \r\n" );
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document.write( "4. Now you have a system of two \r\n" );
document.write( "   equations in two unknowns. Solve\r\n" );
document.write( "   for the two unknowns.\r\n" );
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document.write( "The system we have is \r\n" );
document.write( "\r\n" );
document.write( "      10x  + 9z = 39\r\n" );
document.write( "              x = 3\r\n" );
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document.write( "So we substitute x = 3 in\r\n" );
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document.write( "       10x + 9z = 39\r\n" );
document.write( "     10(3) + 9z = 39\r\n" );
document.write( "        30 + 9z = 39\r\n" );
document.write( "             9z = 9\r\n" );
document.write( "              z = 1  \r\n" );
document.write( "    \r\n" );
document.write( "5. Substitute these values in one of\r\n" );
document.write( "   the original equations to find\r\n" );
document.write( "   the value of the first unknown\r\n" );
document.write( "   eliminated in step 1. \r\n" );
document.write( "\r\n" );
document.write( "I arbitrarily pick the 3rd original\r\n" );
document.write( "equation and substitute x = 3 and\r\n" );
document.write( "z = 1 into:\r\n" );
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document.write( "      x + y + z = 2\r\n" );
document.write( "      3 + y + 1 = 2\r\n" );
document.write( "          4 + y = 2\r\n" );
document.write( "              y = -2\r\n" );
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document.write( "So the solution is:\r\n" );
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document.write( "(x, y, z) = (3, -2, 1)\r\n" );
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document.write( "Edwin
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