document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159312>Question 159312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help on the following problem please? \r<BR>\n" );
document.write( "\n" );
document.write( "problem:<BR>\n" );
document.write( "determine which variable you will substitute for and rewrite as an equation using one variable?\r<BR>\n" );
document.write( "\n" );
document.write( "x + y =6<BR>\n" );
document.write( "2x - 3y =9  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117514 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=117514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> equations are:<BR>\n" );
document.write( "x + y =6<BR>\n" );
document.write( "2x - 3y =9<BR>\n" );
document.write( "-----------------------------------------------------------------<BR>\n" );
document.write( "in the first equation you can solve for x or y in terms of the other.<BR>\n" );
document.write( "it's easier to do this then solving for x or y in the second equation because the calculations look simpler.  i solved for x in terms of y.<BR>\n" );
document.write( "x + y = 6 becomes x = 6 - y so (6-y) is placed in the second equation everywhere that x appears.<BR>\n" );
document.write( "------------------------------------------------------------------<BR>\n" );
document.write( "the second equation of 2*x - 3*y becomes 2*(6-y) -3*y = 9 which becomes 12 - 2*y - 3*y = 9 which becomes 12 - 5*y = 9 which becomes 12 - 9 = 5*y which becomes 3 = 5*y which becomes y = 3/5.<BR>\n" );
document.write( "going back to the first equation x + y = 6, substitute 3/5 for y and the equation becomes x + 3/5 = 6 which becomes x = 6-(3/5) which becomes x = 30/5 - 3/5 which becomes x = 27/5.<BR>\n" );
document.write( "------------------------------------------------------------------<BR>\n" );
document.write( "in the first equation 27/5 + 3/5 = 30/5 = 6 so the first equation checks out ok.<BR>\n" );
document.write( "in the second equation 2*(27/5) - 3*(3/5) = 9 which becomes 54/5 - 9/5 = 9 which becomes 45/5 = 9 which becomes 9 = 9 so the second equation checks out ok as well.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );