document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136905>Question 136905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have tried every solution and I cannot come up with an answer to this problem.<BR>\n" );
document.write( "I am trying to solve the problem by Crammer's Rule using determinants. The problem is: 3x - 2y+ z = 6<BR>\n" );
document.write( "            4x -4y + 3z = 0<BR>\n" );
document.write( "            5x - 4y + z = -5\r<BR>\n" );
document.write( "\n" );
document.write( "I would very much appreciate your help,I have spent hours trying to find solutions to this problem.               Thank-you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #100197 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=100197\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve the problem by Cramer's Rule using determinants. The problem is: <BR>\n" );
document.write( "3x - 2y+ z = 6<BR>\n" );
document.write( "4x -4y + 3z = 0<BR>\n" );
document.write( "5x - 4y + z = -5 <BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "The determinant of the coefficients is:<BR>\n" );
document.write( "[-12-16-30]-[-20-36-8] = -58--64 = 6<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "Replace the \"x-column\" with the constant column to get:<BR>\n" );
document.write( "6...-2...1<BR>\n" );
document.write( "0...-4...3<BR>\n" );
document.write( "-5..-4...1<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "The determinant of that 3 x 3 matrix is:<BR>\n" );
document.write( "[-24+0+30)-(20+-72+0) = 6--52= 58<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Divide the x-determinant by the coefficient determinant to get x = 58/6=29/3<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "To find \"y\":<BR>\n" );
document.write( "1st:Replace the \"y-column\" in the coefficient matrix by the constant column.<BR>\n" );
document.write( "2nd:Find the determinant of this matrix<BR>\n" );
document.write( "3rd:Divide that value by 6 to get the value of \"y\".<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Follow the same pattern for \"z\".<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Final answer:<BR>\n" );
document.write( "x = 29/6<BR>\n" );
document.write( "y = 91/6<BR>\n" );
document.write( "z = 44/6<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );