document.write( "Question 1122204: Find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)
\n" ); document.write( "x + y = 4
\n" ); document.write( "y + z = 4
\n" ); document.write( "x + z = 4
\n" ); document.write( "ax + by + cz = 0
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #738261 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "The  sub-system consisting of 3 (three) first equations has a unique solution x = y = z = 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When you add the fourth equation, it becomes\r\n" );
document.write( "\r\n" );
document.write( "2a + 2b + 2c = 0,   or\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "a + b + c = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus, \r\n" );
document.write( "\r\n" );
document.write( "    a)  if  a + b + c = 0,   then the system of 4 equations has a unique solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    b)  if a + b + c =/= 0,  then the system of 4 equations has no solution.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    c)  it is IMPOSSIBLE to this system to have infinitely many solutions.\r\n" );
document.write( "

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

\n" );