document.write( "Question 440213: The augmented matrix is in row echelon form and represents a linear system. Solve the system by using backward substitution, if possible. Write the solution as either an ordered pair or ordered triple.\r
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Algebra.Com's Answer #304177 by Edwin McCravy(20065) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "This matrix\r\n" );
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document.write( "represents this system of equations:\r\n" );
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document.write( "or written simpler:\r\n" );
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document.write( "The bottom equation\r\n" );
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document.write( "               0z = 0\r\n" );
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document.write( "has ANY real number as a solution.\r\n" );
document.write( "Suppose the number k represents ANY\r\n" );
document.write( "solution to 0z = 0, then  \r\n" );
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document.write( "                z = k\r\n" );
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document.write( "Substitute that into \r\n" );
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document.write( "           y - 4z = 2\r\n" );
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document.write( "           y - 4k = 2\r\n" );
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document.write( "                y = 2 + 4k\r\n" );
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document.write( "Substitute z = k and y = 2 + 4k into\r\n" );
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document.write( "       x - y + 2z = 8\r\n" );
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document.write( "x - (2 + 4k) + 2k = 8\r\n" );
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document.write( "  x - 2 - 4k + 2k = 8\r\n" );
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document.write( "       x - 2 - 2k = 8\r\n" );
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document.write( "                x = 10 + 2k\r\n" );
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document.write( "So the solution is this ordered triple:\r\n" );
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document.write( "(x, y, z) = (10 + 2k, 2 + 4k, k)\r\n" );
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