document.write( "Question 784631: how do I solve this system using Cramer's Rule?
\n" ); document.write( "-3x+4y-z=-1
\n" ); document.write( "5x-2y+3z=-1
\n" ); document.write( "-x+3y-4z=-22 \n" ); document.write( "
Algebra.Com's Answer #477179 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
-3x+4y-z=-1
\n" ); document.write( " 5x-2y+3z=-1
\n" ); document.write( " -x+3y-4z=-22
\n" ); document.write( "
\r\n" );
document.write( "Line up the letters and\r\n" );
document.write( "show all coefficients:\r\n" );
document.write( "\r\n" );
document.write( "-3x + 4y - 1z =  -1\r\n" );
document.write( " 5x - 2y + 3z =  -1\r\n" );
document.write( "-1x + 3y - 4z = -22\r\n" );
document.write( "\r\n" );
document.write( "To solve using Cramer's rule:\r\n" );
document.write( "\r\n" );
document.write( "There are 4 columns,\r\n" );
document.write( "\r\n" );
document.write( "1. The column of x-coefficients \"matrix%283%2C1%2C-3%2C5%2C-1%29\"\r\n" );
document.write( "\r\n" );
document.write( "2. The column of y-coefficients \"matrix%283%2C1%2C4%2C-2%2C3%29\"\r\n" );
document.write( "\r\n" );
document.write( "3. The column of z-coefficients \"matrix%283%2C1%2C-1%2C3%2C-4%29\"\r\n" );
document.write( "\r\n" );
document.write( "4. The column of constants:     \"red%28matrix%283%2C1%2C-1%2C-1%2C-22%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "There are four determinants:\r\n" );
document.write( "\r\n" );
document.write( "1. The determinant \"D\" consists of just the three columns\r\n" );
document.write( "of x, y, and z coefficients. in that order, but does not\r\n" );
document.write( "contain the column of constants.\r\n" );
document.write( "\r\n" );
document.write( "\"D=abs%28matrix%283%2C3%2C-3%2C4%2C-1%2C5%2C-2%2C3%2C-1%2C3%2C-4%29%29\".\r\n" );
document.write( "\r\n" );
document.write( "It has value \"D=58\".  I'm assuming you know how to find the\r\n" );
document.write( "value of a 3x3 determinant, for that's a subject all by itself.\r\n" );
document.write( "If you don't know how, post again asking how.\r\n" );
document.write( "\r\n" );
document.write( "2. The determinant \"D%5Bx%5D\" is like the determinant \"D\"\r\n" );
document.write( "except that the column of x-coefficients is replaced by the\r\n" );
document.write( "column of constants.  \"D%5Bx%5D\" does not contain the column\r\n" );
document.write( "of x-coefficients.\r\n" );
document.write( "\r\n" );
document.write( ".\r\n" );
document.write( "\r\n" );
document.write( "It has value \"D%5Bx%5D=-232\".\r\n" );
document.write( "\r\n" );
document.write( "3. The determinant \"D%5By%5D\" is like the determinant \"D\"\r\n" );
document.write( "except that the column of y-coefficients is replaced by the\r\n" );
document.write( "column of constants.  \"D%5By%5D\" does not contain the column\r\n" );
document.write( "of y-coefficients.\r\n" );
document.write( "\r\n" );
document.write( ".\r\n" );
document.write( "\r\n" );
document.write( "It has value \"D%5By%5D=-116\".\r\n" );
document.write( "\r\n" );
document.write( "4. The determinant \"D%5Bz%5D\" is like the determinant \"D\"\r\n" );
document.write( "except that the column of z-coefficients is replaced by the\r\n" );
document.write( "column of constants.  \"D%5Bz%5D\" does not contain the column\r\n" );
document.write( "of z-coefficients.\r\n" );
document.write( "\r\n" );
document.write( ".\r\n" );
document.write( "\r\n" );
document.write( "It has value \"D%5Bx%5D=-150\".\r\n" );
document.write( "\r\n" );
document.write( "Now the formulas for x, y and z are\r\n" );
document.write( "\r\n" );
document.write( "\"x=D%5Bx%5D%2FD=%28-232%29%2F%2858%29=-4\"\r\n" );
document.write( "\"y=D%5By%5D%2FD=%28-116%29%2F%2858%29=-2\"\r\n" );
document.write( "\"x=D%5Bz%5D%2FD=%28290%29%2F%2858%29=5\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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