document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=121386>Question 121386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to solve the following systems of three equations<BR>\n" );
document.write( "      x+y+z=5<BR>\n" );
document.write( "      x-y+z=1<BR>\n" );
document.write( "      x-z=y+3<BR>\n" );
document.write( "Thank you so very much  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89180 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x+y+z=5<BR>\n" );
document.write( "x-y+z=1<BR>\n" );
document.write( "x-y-z=3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You didn't specify a solution method. <BR>\n" );
document.write( "Hopefully a matrix solution is OK.<BR>\n" );
document.write( "[A][x]=[b]<BR>\n" );
document.write( "where<BR>\n" );
document.write( "[A]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C3%2C%0D%0A1%2C1%2C1%2C%0D%0A1%2C-1%2C1%2C%0D%0A1%2C-1%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C3%2C%0D%0A1%2C1%2C1%2C%0D%0A1%2C-1%2C1%2C%0D%0A1%2C-1%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[x]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C1%2Cx%2Cy%2Cz%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[b]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C1%2C5%2C1%2C3%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C1%2C5%2C1%2C3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We then need to find the inverse of [A]([Ainv]) and matrix multiply by [b] to get [x].<BR>\n" );
document.write( "[A][x]=[b]<BR>\n" );
document.write( "[x]=[Ainv][b]<BR>\n" );
document.write( "[Ainv]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2A%28matrix%283%2C3%2C%0D%0A2%2C0%2C2%2C%0D%0A2%2C-2%2C0%2C%0D%0A0%2C2%2C-2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[Ainv][b]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29%2A%28matrix%283%2C3%2C%0D%0A2%2C0%2C2%2C%0D%0A2%2C-2%2C0%2C%0D%0A0%2C2%2C-2%29%29%2A%28matrix%283%2C1%2C5%2C1%2C3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[x]=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%283%2C1%2C4%2C2%2C-1%29%29 ALIGN=MIDDLE  ALT=\"%28matrix%283%2C1%2C4%2C2%2C-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x=4<BR>\n" );
document.write( "y=2<BR>\n" );
document.write( "z=-1 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );