document.write( "Question 1090282: 3x+5y-z+2=0
\n" ); document.write( "4x-y+2z-1=0
\n" ); document.write( "-6xx-10y+2z=0
\n" ); document.write( "use gaussian reduction method to solve the following linear equation \n" ); document.write( "

Algebra.Com's Answer #704758 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "3x+5y-z+2=0
\n" ); document.write( "4x-y+2z-1=0
\n" ); document.write( "-6xx-10y+2z=0
\n" ); document.write( "use gaussian reduction method to solve the following linear equation
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "1.  The third equation contains a mistake. It should not contain xx. It must be x instead.\r\n" );
document.write( "\r\n" );
document.write( "    Therefore, I re-write the system in correct form\r\n" );
document.write( "\r\n" );
document.write( "     3x +  5y -  z + 2 = 0,\r\n" );
document.write( "     4x -   y + 2z - 1 = 0,\r\n" );
document.write( "    -6x - 10y + 2z = 0.\r\n" );
document.write( "\r\n" );
document.write( "    And rewrite it one more time in the standard form:\r\n" );
document.write( "\r\n" );
document.write( "     3x +  5y -  z = -2,    (1)\r\n" );
document.write( "     4x -   y + 2z =  1,    (2)\r\n" );
document.write( "    -6x - 10y + 2z =  0.    (3)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  Now notice that the left side of the equation (3) is exactly two times left side of the equation (1). \r\n" );
document.write( "    While the right side terms ARE NOT in this proportion.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    It means that the system (1),(2),(3) is INCONSISTENT, i.e. HAS NO solutions,\r\n" );
document.write( "\r\n" );
document.write( "    Therefore, the original system, as equivalent to (1),(2),(3), HAS NO solutions as well.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  The original system is inconsistent and does not have solutions.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );