document.write( "Question 1175288: Given the system of equations\r
\n" ); document.write( "\n" ); document.write( "(2x - 3y - 9z = -24
\n" ); document.write( "|x + 3z = 6
\n" ); document.write( "|-3x + y - 4z = -6
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\n" ); document.write( "\n" ); document.write( "(a) determine whether the system is inconsistent or dependent;
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\n" ); document.write( "\n" ); document.write( "(b) if your answer is dependent in (a), find the complete solution. Write
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Algebra.Com's Answer #801059 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Since y is already eliminated from the middle equation, eliminate y\r\n" );
document.write( "from the first and third equations by multiplying the third one by 3,\r\n" );
document.write( "and adding term by term:\r\n" );
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document.write( " 2x - 3y -  9z = -24\r\n" );
document.write( "-9x + 3y - 12z = -18\r\n" );
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document.write( "-7x      - 21z = -42\r\n" );
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document.write( "Let's divide that through by -7\r\n" );
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document.write( " x + 3z = 6\r\n" );
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document.write( "That's the same as the 2nd equation, so it is a dependent system.\r\n" );
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document.write( "Solve that for x:\r\n" );
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document.write( "x = 6 - 3z\r\n" );
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document.write( "Substitute that in either of the other two original equations.  I'll pick\r\n" );
document.write( "the first one:\r\n" );
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document.write( "       -3x + y - 4z = -6\r\n" );
document.write( "-3(6 - 3z) + y - 4z = -6\r\n" );
document.write( "  -18 + 9z + y - 4z = -6\r\n" );
document.write( "       -18 + 5z + y = -6\r\n" );
document.write( "                  y = 12 - 5z\r\n" );
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document.write( "Solution:   (x, y, z) = (6 - 3z, 12 - 5z, z)\r\n" );
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document.write( "Edwin

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