document.write( "Question 92959This question is from textbook
\n" ); document.write( ": The following matrix is obtained from a system of equations
\n" ); document.write( "\"%28matrix%283%2C4%2C+1%2C+0%2C+6%2C+5%2C+0%2C+1%2C+-4%2C+3%2C0%2C+0%2C++2%2C+-6%29%29+\" \r
\n" ); document.write( "\n" ); document.write( "The solution to the system is ___________.
\n" ); document.write( "

Algebra.Com's Answer #67681 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
The following matrix is obtained from a system of equations
\n" ); document.write( "\"%28matrix%283%2C4%2C+1%2C+0%2C+6%2C+5%2C+0%2C+1%2C+-4%2C+3%2C0%2C+0%2C++2%2C+-6%29%29+\" \r
\n" ); document.write( "\n" ); document.write( "The solution to the system is ___________.
\n" ); document.write( "
\r\n" );
document.write( "This matrix is an abbreviation for\r\n" );
document.write( "\r\n" );
document.write( "1x + 0x + 6z =  5\r\n" );
document.write( "0x + 1y - 4z =  3\r\n" );
document.write( "0x + 0y + 2z = -6\r\n" );
document.write( "\r\n" );
document.write( "or, after erasing the 0 terms and the \r\n" );
document.write( "1 coefficients:\r\n" );
document.write( "\r\n" );
document.write( " x      + 6z =  5\r\n" );
document.write( "      y - 4z =  3\r\n" );
document.write( "          2z = -6\r\n" );
document.write( "\r\n" );
document.write( "Solve the bottom equation for z\r\n" );
document.write( "\r\n" );
document.write( "          2z = -6\r\n" );
document.write( "           z = -3\r\n" );
document.write( "\r\n" );
document.write( "Substitute that in the middle equation:\r\n" );
document.write( "\r\n" );
document.write( "      y - 4z =  3\r\n" );
document.write( "   y - 4(-3) =  3\r\n" );
document.write( "      y + 12 =  3\r\n" );
document.write( "           y = -9\r\n" );
document.write( "\r\n" );
document.write( "Substitute z = -3 in the top equation:\r\n" );
document.write( "\r\n" );
document.write( " x      + 6z =  5\r\n" );
document.write( "      x + 6z = 5\r\n" );
document.write( "   x + 6(-3) = 5\r\n" );
document.write( "      x - 18 = 5\r\n" );
document.write( "           x = 23\r\n" );
document.write( "\r\n" );
document.write( "So the solution is\r\n" );
document.write( "\r\n" );
document.write( "(x, y, z) = (23, -9, -3)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );