document.write( "Question 152205:
\r\n" ); document.write( "Write the system of linear equations, use x,y,z and if necessary w,x,y,z.\r\n" ); document.write( "Once system is written, use back-substitution to find its solution: \r\n" ); document.write( "\r\n" ); document.write( "|1 2 -1 0 | 2|\r\n" ); document.write( "|0 1 1 -2 | -3|\r\n" ); document.write( "|0 0 1 -1 | -2|\r\n" ); document.write( "|0 0 0 1 | 3|\r\n" ); document.write( "
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Algebra.Com's Answer #111965 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Write the system of linear equations, use x,y,z and if necessary w,x,y,z. \r\n" );
document.write( "Once system is written, use back-substitution to find its solution: \r\n" );
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document.write( "|1  2 -1  0 |  2|\r\n" );
document.write( "|0  1  1 -2 | -3|\r\n" );
document.write( "|0  0  1 -1 | -2|\r\n" );
document.write( "|0  0  0  1 |  3|\r\n" );
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document.write( "Put w's after the numbers in the first column:\r\n" );
document.write( "Put x's after the numbers in the second column:\r\n" );
document.write( "Put y's after the numbers in the third column:\r\n" );
document.write( "Put z's after the numbers in the fourth column:\r\n" );
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document.write( "|1w 2x-1y 0z|  2|\r\n" );
document.write( "|0w 1x 1y-2z| -3|\r\n" );
document.write( "|0w 0x 1y-1z| -2|\r\n" );
document.write( "|0w 0x 0y 1z|  3|\r\n" );
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document.write( "Put in + signs between terms if there's not a \r\n" );
document.write( "sign between them\r\n" );
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document.write( "|1w+2x-1y+0z|  2|\r\n" );
document.write( "|0w+1x+1y-2z| -3|\r\n" );
document.write( "|0w+0x+1y-1z| -2|\r\n" );
document.write( "|0w+0x+0y+1z|  3|\r\n" );
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document.write( "Replace all the \"|\" after the z's with equal signs:\r\n" );
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document.write( "|1w+2x-1y+0z=  2|\r\n" );
document.write( "|0w+1x+1y-2z= -3|\r\n" );
document.write( "|0w+0x+1y-1z= -2|\r\n" );
document.write( "|0w+0x+0y+1z=  3|\r\n" );
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document.write( "Erase all the terms with a 0 coefficient:\r\n" );
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document.write( "|1w+2x-1y   =  2|\r\n" );
document.write( "|   1x+1y-2z= -3|\r\n" );
document.write( "|      1y-1z= -2|\r\n" );
document.write( "|         1z=  3|\r\n" );
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document.write( "Erase all the 1 coefficients:\r\n" );
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document.write( "| w+2x- y   =  2|\r\n" );
document.write( "|    x+ y-2z= -3|\r\n" );
document.write( "|       y- z= -2|\r\n" );
document.write( "|          z=  3|\r\n" );
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document.write( "Write as a system of equations:\r\n" );
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document.write( "Now we do back substitution, starting at\r\n" );
document.write( "the bottom with  and substitute \r\n" );
document.write( "that in  \r\n" );
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document.write( "Now we substitute  and  in\r\n" );
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document.write( "Finally we substitute  and  in\r\n" );
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document.write( "So the solution is (w,x,y,z) = (-1,2,1,3)\r\n" );
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document.write( "Edwin

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