document.write( "Question 44504: Solve the system of equations.\r
\n" ); document.write( "\n" ); document.write( "7x + 7y + z = 1\r
\n" ); document.write( "\n" ); document.write( "x + 8y + 8z = 8\r
\n" ); document.write( "\n" ); document.write( "9x + y + 9z = 9 \n" ); document.write( "
Algebra.Com's Answer #29392 by AnlytcPhil(1806)\"\" \"About 
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7x + 7y +  z = 1 \r\n" );
document.write( " x + 8y + 8z = 8 \r\n" );
document.write( "9x +  y + 9z = 9 \r\n" );
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document.write( "1. Pick two equations and pick a letter to eliminate.\r\n" );
document.write( "2. Eliminate that letter from the two equations you picked.\r\n" );
document.write( "3. Pick two other equations and eliminate the SAME LETTER that\r\n" );
document.write( "   you eliminated in step 2.\r\n" );
document.write( "4. Now you have two equations in two unknowns.\r\n" );
document.write( "5. Solve that system in two unknowns. You will have values for\r\n" );
document.write( "   two of the three unknowns.\r\n" );
document.write( "6. Substitute these values into one of the original equations\r\n" );
document.write( "   to find the third letter, the one you eliminated in step 1.\r\n" );
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document.write( "1. Pick two equations and pick a letter to eliminate.\r\n" );
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document.write( "7x + 7y +  z = 1 \r\n" );
document.write( " x + 8y + 8z = 8 \r\n" );
document.write( "9x +  y + 9z = 9\r\n" );
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document.write( "I will arbitrarily pick the first and third equations and the \r\n" );
document.write( "letter y to eliminate. \r\n" );
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document.write( "2. Eliminate that letter from the two equations you picked.\r\n" );
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document.write( " Multiply the first by -1 and the second by\r\n" );
document.write( "7:\r\n" );
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document.write( "-1[7x + 7y +  z = 1]  \r\n" );
document.write( " 7[9x +  y + 9z = 9]\r\n" );
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document.write( "-7x - 7y -   z = -1\r\n" );
document.write( "56x + 7y + 63z = 63\r\n" );
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document.write( "49x      + 62z = 62\r\n" );
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document.write( "3. Pick two other equations and eliminate the SAME LETTER that\r\n" );
document.write( "   you eliminated in step 2.\r\n" );
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document.write( "I will now pick the first and second equations.  I must \r\n" );
document.write( "eliminate the same letter y to eliminate.  Multiply the first\r\n" );
document.write( "by -1 and the second by 8:\r\n" );
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document.write( " x + 8y + 8z = 8 \r\n" );
document.write( "9x +  y + 9z = 9\r\n" );
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document.write( "-1[ x + 8y + 8z = 8]  \r\n" );
document.write( " 8[9x +  y + 9z = 9]\r\n" );
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document.write( " -x - 8y -  8z = -8\r\n" );
document.write( "72x + 8y + 72z = 72\r\n" );
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document.write( "71x      + 64z = 64\r\n" );
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document.write( "4. Now you have two equations in two unknowns.\r\n" );
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document.write( "49x + 62z = 62\r\n" );
document.write( "71x + 64z = 64\r\n" );
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document.write( "5. Solve that system in two unknowns. \r\n" );
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document.write( "Eliminate x by multiplying the first equation by\r\n" );
document.write( "-71 and the seciond equation by 49\r\n" );
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document.write( "-71[49x + 62z = 62]\r\n" );
document.write( " 49[71x + 64z = 64]\r\n" );
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document.write( "-3479x - 4402z = -4402\r\n" );
document.write( " 3479x + 3136z =  3136\r\n" );
document.write( "----------------------\r\n" );
document.write( "        -1266z = -1266\r\n" );
document.write( "             z = 1\r\n" );
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document.write( "Substitute z = 1 into 49x + 62z = 62\r\n" );
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document.write( "     49x + 62z = 62\r\n" );
document.write( "   49x + 62(1) = 62\r\n" );
document.write( "      49x + 62 = 62\r\n" );
document.write( "           49x =  0\r\n" );
document.write( "             x =  0\r\n" );
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document.write( "  You now have values for\r\n" );
document.write( "   two of the three unknowns.\r\n" );
document.write( "6. Substitute these values into one of the original equations\r\n" );
document.write( "   to find the third letter, the one you eliminated in step 1.\r\n" );
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document.write( "Substitute z = 1 and x = 0 into the third original equation\r\n" );
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document.write( "        9x +  y + 9z = 9\r\n" );
document.write( "     9(1) + y + 9(0) = 9\r\n" );
document.write( "           9 + y + 0 = 9\r\n" );
document.write( "               9 + y = 9\r\n" );
document.write( "                   y = 0\r\n" );
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document.write( "Solution: (x, y, z) = (0, 0, 1) \r\n" );
document.write( "              \r\n" );
document.write( "Edwin
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