document.write( "Question 33856: How do I solve\r
\n" ); document.write( "\n" ); document.write( "x +3y -6z =7
\n" ); document.write( "2x -y +z =1
\n" ); document.write( "x +2y + 2z =1\r
\n" ); document.write( "\n" ); document.write( "Thanks,
\n" ); document.write( "Tijuana \n" ); document.write( "

Algebra.Com's Answer #20271 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

 x + 3y - 6z = 7   \r\n" );
document.write( "2x -  y +  z = 1 \r\n" );
document.write( " x + 2y + 2z = 1\r\n" );
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document.write( "1.  Use the 1st equation to eliminate x from the 2nd equation.\r\n" );
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document.write( "2.  Use the 1st equation to eliminate x from the 3rd equation.\r\n" );
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document.write( "3.  Use the 2nd equation to eliminate y from the 3rd equation.\r\n" );
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document.write( "4.  Solve the 3rd equation for z.\r\n" );
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document.write( "5.  Substitute the value of z in the 2nd equation to find y.\r\n" );
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document.write( "6. Substitute the values of y and z in the 1st equation to solve \r\n" );
document.write( "   for x.\r\n" );
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document.write( " x + 3y - 6z = 7  \r\n" );
document.write( "2x -  y +  z = 1 \r\n" );
document.write( " x + 2y + 2z = 1\r\n" );
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document.write( "Get rid of the 2x by adding -2 times the 1st equation to \r\n" );
document.write( "1 times the 2nd:\r\n" );
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document.write( "-2[ x + 3y - 6z = 7]  \r\n" );
document.write( " 1[2x -  y +  z = 1] \r\n" );
document.write( "    x + 2y + 2z = 1\r\n" );
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document.write( " x + 3y -  6z =   7  \r\n" );
document.write( "    -7y + 13z = -13\r\n" );
document.write( " x + 2y +  2z =   1\r\n" );
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document.write( "Get rid of the x on the bottom left by adding -1 times the \r\n" );
document.write( "1st equation to 1 times the 3rd:\r\n" );
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document.write( " -1[x + 3y -  6z =   7   \r\n" );
document.write( "       -7y + 13z = -13\r\n" );
document.write( "  1[x + 2y +  2z =   1\r\n" );
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document.write( " x + 3y -  6z =   7   \r\n" );
document.write( "    -7y + 13z = -13\r\n" );
document.write( "     -y +  8z =  -6\r\n" );
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document.write( "Get rid of the -y on the by adding -1 times the \r\n" );
document.write( "2nd equation to 7 times the 3rd:\r\n" );
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document.write( "    x + 3y -  6z =   7   \r\n" );
document.write( "-1[    -7y + 13z = -13\r\n" );
document.write( " 7[    -y +  8z =  -6\r\n" );
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document.write( " x + 3y -  6z =   7   \r\n" );
document.write( "    -7y + 13z = -13\r\n" );
document.write( "          43z = -29\r\n" );
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document.write( "Solve the bottom equation for z and get z = -29/43\r\n" );
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document.write( "Replace z by -29/43 in the second equation\r\n" );
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document.write( "-7y + 13(-29/43) = -13\r\n" );
document.write( "Clear of fractions by multiplying by 43\r\n" );
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document.write( "-301y - 377 = -559\r\n" );
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document.write( "-301y = -182\r\n" );
document.write( "    y = -182/(-301) = 26/43\r\n" );
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document.write( "Replace y by 26/43 and z by -29/43 in the 1st equation:\r\n" );
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document.write( "       x + 3y -  6z =   7\r\n" );
document.write( "        x +  3(26/43) - 6(-29/43) = 7\r\n" );
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document.write( "Clear of fractions by multiplying through by 43\r\n" );
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document.write( "         43x + 78 + 174 = 301\r\n" );
document.write( "              43x + 252 = 301\r\n" );
document.write( "                    43x =  49    \r\n" );
document.write( "                      x = 49/43\r\n" );
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document.write( "So x = 49/43, y = 26/43, z = -29/43\r\n" );
document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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