document.write( "Question 270365: A student says that the system consisting of x=0, y=0, and z=0 has no solutions. Explain the student's error. Write and solve a system. \n" ); document.write( "
Algebra.Com's Answer #198079 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The student's error is that 0 is a number,\r\n" );
document.write( "and therefore is a perfectly good answer.\r\n" );
document.write( "\r\n" );
document.write( "This system\r\n" );
document.write( "\r\n" );
document.write( "\"system%28x%2By%2Bz=0%2Cx-y%2Bz=0%2Cx%2By-z=0%29\"\r\n" );
document.write( "\r\n" );
document.write( "We can eliminate y by adding the first two equations\r\n" );
document.write( "just as they are:\r\n" );
document.write( "\r\n" );
document.write( " x + y + z = 0\r\n" );
document.write( " x - y + z = 0\r\n" );
document.write( " -------------\r\n" );
document.write( "2x     +2z = 0 \r\n" );
document.write( "\r\n" );
document.write( "We can eliminate y and z by adding the last two equations:\r\n" );
document.write( "\r\n" );
document.write( " x - y + z = 0\r\n" );
document.write( " x + y - z = 0\r\n" );
document.write( " -------------\r\n" );
document.write( "2x         = 0\r\n" );
document.write( "\r\n" );
document.write( "So we have the system:\r\n" );
document.write( "\r\n" );
document.write( "\"system%282x%2B2z=0%2C2x=0%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve the second one for s, \r\n" );
document.write( "\r\n" );
document.write( "2x = 0\r\n" );
document.write( " x = 0\r\n" );
document.write( "\r\n" );
document.write( "Substitute in \r\n" );
document.write( "\r\n" );
document.write( " 2x  + 2z = 0\r\n" );
document.write( "2(0) + 2z = 0\r\n" );
document.write( "       2z = 0\r\n" );
document.write( "        z = 0\r\n" );
document.write( "\r\n" );
document.write( "Substitute in one of the original equations:\r\n" );
document.write( "\r\n" );
document.write( "x + y + z = 0\r\n" );
document.write( "0 + y + 0 = 0\r\n" );
document.write( "        y = 0\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );