document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164189>Question 164189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve the system: <BR>\n" );
document.write( "5x-3y+z=-7<BR>\n" );
document.write( "4x+5y+3z=-2<BR>\n" );
document.write( "2x-3y+5z=22<BR>\n" );
document.write( "show work and i think you can solve it in the calculator by matrices right?<BR>\n" );
document.write( "if you know both ways please show thanks!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121996 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve the system: <BR>\n" );
document.write( "5x-3y+z=-7<BR>\n" );
document.write( "4x+5y+3z=-2<BR>\n" );
document.write( "2x-3y+5z=22<BR>\n" );
document.write( "show work and i think you can solve it in the calculator by matrices right?<BR>\n" );
document.write( "if you know both ways please show thanks!<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "You can do it by elimination and substitution, but that's tedious and error prone.<BR>\n" );
document.write( "If you calculator has the functionality, you can do a matrix solution on it.<BR>\n" );
document.write( "I have an Excel sheet that does it using determinants.<BR>\n" );
document.write( "By Excel:<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "y = -1<BR>\n" );
document.write( "z = +5<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Using elimination and substitution:<BR>\n" );
document.write( "5x-3y+z=-7  eqn 1<BR>\n" );
document.write( "4x+5y+3z=-2 eqn 2<BR>\n" );
document.write( "2x-3y+5z=22 eqn 3<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Eqn 1 has a z coeff of 1, so muliply it by 3, and then by 5.<BR>\n" );
document.write( "5x-3y+z=-7<BR>\n" );
document.write( "15x - 9y + 3z = -21  eqn 1 times 3<BR>\n" );
document.write( " 4x + 5y + 3z = -2   eqn 2<BR>\n" );
document.write( "11x - 14y = -19   Subtract eqn 2<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "5x-3y+z=-7  eqn 1 again<BR>\n" );
document.write( "25x - 15y + 5z = -35  eqn 1 times 5<BR>\n" );
document.write( " 2x -  3y + 5z = 22   eqn 3<BR>\n" );
document.write( "23x - 12y  = -57  Subract eqn 3<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Now there are 2 eqns in 2 unknowns (x and y)<BR>\n" );
document.write( "11x - 14y = -19<BR>\n" );
document.write( "23x - 12y = -57<BR>\n" );
document.write( "Multiply the 1st times 6, and the 2nd times 7 to get the same coeff for y.<BR>\n" );
document.write( "66x - 84y = -114<BR>\n" );
document.write( "161x -84y = -399   Subtract <BR>\n" );
document.write( "-95x = 285<BR>\n" );
document.write( "x = -3<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Sub into 11x - 14y = -19 to get<BR>\n" );
document.write( "y = -1<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Sub x and y into any of the original 3 eqns to get <BR>\n" );
document.write( "z = +5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );