document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=551877>Question 551877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the echelon method to solve:<BR>\n" );
document.write( "x+y=16<BR>\n" );
document.write( "6x-y=33<BR>\n" );
document.write( "cant seem to get it right </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #360000 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=360000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have not heard of an echelon method, but I have heard translations of the word echelon from the French into other languages to refer to a strategy to solve systems of linear equations.<BR>\n" );
document.write( "You want to keep an equation involving both variables and replace the other equation with a combination of the two where one of the variables has been eliminated.<BR>\n" );
document.write( "I would keep <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=16 ALIGN=MIDDLE  ALT=\"x%2By=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > because it's nice and simple and replace the other equation, using the sum of the two<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By%2B6x-y=16%2B33 ALIGN=MIDDLE  ALT=\"x%2By%2B6x-y=16%2B33\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=49 ALIGN=MIDDLE  ALT=\"7x=49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The system is now<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=16 ALIGN=MIDDLE  ALT=\"x%2By=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=49 ALIGN=MIDDLE  ALT=\"7x=49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Even better, we can further simplify, dividing both sides by 7.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7x=49 ALIGN=MIDDLE  ALT=\"7x=49\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we could say that we now have the system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=16 ALIGN=MIDDLE  ALT=\"x%2By=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then substituting we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2By=16 ALIGN=MIDDLE  ALT=\"7%2By=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16-7=9 ALIGN=MIDDLE  ALT=\"y=16-7=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Maybe you were trying to eliminate instead of y to give your modified system the same shape as the one in the book.<BR>\n" );
document.write( "We can do that too, if you get points for eliminating variables in alphabetical order.<BR>\n" );
document.write( "Just multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=16 ALIGN=MIDDLE  ALT=\"x%2By=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > times -6 to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-6y=-96 ALIGN=MIDDLE  ALT=\"-6x-6y=-96\"   DISABLED_style= \"max-width:90%; height:auto;\" > and add it to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x-y=33 ALIGN=MIDDLE  ALT=\"6x-y=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6x-6y%2B6x-y=-96%2B33 ALIGN=MIDDLE  ALT=\"-6x-6y%2B6x-y=-96%2B33\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7y=-63 ALIGN=MIDDLE  ALT=\"-7y=-63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then you could simplify it by dividing both sides by -7 to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=9 ALIGN=MIDDLE  ALT=\"y=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );