document.write( "Question 1035366: Show that the following system is consistent if and only if c=2a-3b and solve the system in this case
\n" ); document.write( " 2x-y+3z=a
\n" ); document.write( " 3x+y-5z=b
\n" ); document.write( " -5x-5y+21z=c
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Algebra.Com's Answer #650052 by Edwin McCravy(20054) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "We procede as though we were going to solve the\r\n" );
document.write( "system by the Gauss-Jordan method:\r\n" );
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document.write( "The augmented matrix is\r\n" );
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document.write( "Get a 0 where the 3 is on the 2nd row 1st column,\r\n" );
document.write( "by row operation -3R1+2R2->R2\r\n" );
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document.write( "Get a 0 where the -5 is on the 3rd row 1st column,\r\n" );
document.write( "by row operation 5R1+2R3->R3\r\n" );
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document.write( "Get a 0 where the -15 is on the 3rd row 2nd column,\r\n" );
document.write( "by row operation 3R2+R3->R3\r\n" );
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document.write( "That last row is equivalent to the equation\r\n" );
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document.write( "That can be true and thus the system is \r\n" );
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document.write( "consistent if and only if\r\n" );
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document.write( "Solving for c gives\r\n" );
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document.write( "I'll let you finish solving the system.\r\n" );
document.write( "If you have trouble, tell me in the \r\n" );
document.write( "thank-you note form below and I'll get\r\n" );
document.write( "back to you by email.  There is no\r\n" );
document.write( "charge because I just do this as a hobby.\r\n" );
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document.write( "Edwin

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