document.write( "Question 814179: Solve the following by gauss elimination method?
\n" ); document.write( "5x+3y+7z=4
\n" ); document.write( "3x+26y+2z=9
\n" ); document.write( "7x+2y+10z=5 \n" ); document.write( "

Algebra.Com's Answer #490166 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( " 5     3     7     4\r\n" );
document.write( " 3    26     2     9\r\n" );
document.write( " 7     2    10     5\r\n" );
document.write( "Multiply row 1 by 1/5:\r\n" );
document.write( " 1   3/5   7/5   4/5\r\n" );
document.write( " 3    26     2     9\r\n" );
document.write( " 7     2    10     5\r\n" );
document.write( "Add -3 times row 1 to row 2:\r\n" );
document.write( " 1    3/5   7/5   4/5\r\n" );
document.write( " 0  121/5 -11/5  33/5\r\n" );
document.write( " 7     2    10     5\r\n" );
document.write( "Add -7 times row 1 to row 3:\r\n" );
document.write( " 1    3/5   7/5   4/5\r\n" );
document.write( " 0  121/5 -11/5  33/5\r\n" );
document.write( " 0  -11/5   1/5  -3/5\r\n" );
document.write( "Multiply row 2 by 5/121:\r\n" );
document.write( " 1    3/5   7/5   4/5\r\n" );
document.write( " 0      1 -1/11  3/11\r\n" );
document.write( " 0  -11/5   1/5  -3/5\r\n" );
document.write( "Add -3/5 times row 2 to row 1:\r\n" );
document.write( " 1      0  16/11  7/11\r\n" );
document.write( " 0      1  -1/11  3/11\r\n" );
document.write( " 0  -11/5   1/5  -3/5\r\n" );
document.write( "Add 11/5 times row 2 to row 3:\r\n" );
document.write( " 1      0  16/11  7/11\r\n" );
document.write( " 0      1  -1/11  3/11\r\n" );
document.write( " 0      0    0     0\r\n" );
document.write( "

This is as far as we can go. This translates into:
\n" ); document.write( " x + (16/11)z = 7/11 or x = (-16/11)z + 7/11
\n" ); document.write( " y - (1/11)z = 3/11 or y = (1/11)z + 3/11
\n" ); document.write( "So there are an infinite number of solutions. One way to express the solution would be:
\n" ); document.write( "((-16/11)z + 7/11, (1/11)z + 3/11, z) where z is any real number. \n" ); document.write( "

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