document.write( "Question 1090883: Please help me with this, I tried to solve it, but cannot get the solution
\n" ); document.write( "Solve the system for x,y,z
\n" ); document.write( "2x+3y-z=4
\n" ); document.write( "3x-y+2z=5
\n" ); document.write( "x-4y+3z=1
\n" ); document.write( "Thank you. \n" ); document.write( "
Algebra.Com's Answer #705328 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "This system turns out to be a dependent system which has\r\n" );
document.write( "infinitely many solutions.  I'll show you below how to\r\n" );
document.write( "do it on your TI-83 or TI-84 calculator.  If you need\r\n" );
document.write( "help on how to solve it without a calculator, just say\r\n" );
document.write( "so in the thank-you note form below and I'll help you\r\n" );
document.write( "do it by the matrix method without a calculator.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "----------------------------------\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Put all those red numbers in a 3x4 augmented matrix\r\n" );
document.write( "like this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "On your TI-83 or TI-84,\r\n" );
document.write( "\r\n" );
document.write( "Press CLEAR\r\n" );
document.write( "\r\n" );
document.write( "Press 2ND\r\n" );
document.write( "Press x-1 (MATRIX)\r\n" );
document.write( "Prees the right arrow twice to highlight EDIT\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Press 2\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Press 3\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Type -1, \r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Type 4,\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Type 3,\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Type -1\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Type 2\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "...\r\n" );
document.write( "continue typing in all the rest of the elements \r\n" );
document.write( "in the matrix, pressing ENTER after each. Then\r\n" );
document.write( "...\r\n" );
document.write( "Press 2ND\r\n" );
document.write( "Press MODE (QUIT)\r\n" );
document.write( "Press 2ND\r\n" );
document.write( "Press x-1 (MATRIX)\r\n" );
document.write( "Press right arrow to highlight MATH\r\n" );
document.write( "Press up arrow 5 times to highlight B:rref(\r\n" );
document.write( "Press ENTER  you should see rref( on the screen\r\n" );
document.write( "Press 2nd\r\n" );
document.write( "Press x-1 (MATRIX)\r\n" );
document.write( "Press ENTER  you should see rref([A]\r\n" );
document.write( "Type )\r\n" );
document.write( "Press MATH\r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Press Enter\r\n" );
document.write( "You should see  \r\n" );
document.write( "\r\n" );
document.write( "rref([A]\r\n" );
document.write( "    [[1 0 5/11  19/11]\r\n" );
document.write( "     [0 1 -7/11 2/11 ]\r\n" );
document.write( "     [0 0       0    ]]\r\n" );
document.write( "\r\n" );
document.write( "Interpret this as the system:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's the same as\r\n" );
document.write( "\r\n" );
document.write( "\"system%28x%2Bexpr%285%2F11%29z=19%2F11%2C%0D%0Ay-expr%287%2F11%29z=2%2F11%2C%0D%0A0%2Az=0%29\"\r\n" );
document.write( "\r\n" );
document.write( "Notice that the third equation 0*z=0 is such that\r\n" );
document.write( "z can be any number whatever, for any number\r\n" );
document.write( "substituted for z in 0*z=0 will always give 0=0.\r\n" );
document.write( "So let a = any number.\r\n" );
document.write( "Since z = any number, we substitute a for z\r\n" );
document.write( "\r\n" );
document.write( "\"system%28x%2Bexpr%285%2F11%29a=19%2F11%2C%0D%0Ay-expr%287%2F11%29a=2%2F11%2C%0D%0A0%2Aa=0%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the first for x, the second for y,\r\n" );
document.write( "then write z = a\r\n" );
document.write( "\r\n" );
document.write( "\"system%28x=19%2F11-expr%285%2F11%29a%2C%0D%0Ay=2%2F11%2Bexpr%287%2F11%29a%2C%0D%0Az=a%29\"\r\n" );
document.write( "\r\n" );
document.write( "So the general solution is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We can get as many solutions as we like by choosing \r\n" );
document.write( "different values for the number \"a\".  For instance,\r\n" );
document.write( "if we choose a = -5, we have the solution\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and if we choose a = 6, we have the solution\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
 \n" );
document.write( "
\n" );