document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173516>Question 173516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need help with-     <BR>\n" );
document.write( "x+y=9 <BR>\n" );
document.write( "y=2x when the directions say solve by graphing and substitution<BR>\n" );
document.write( " 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 #128395 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=128395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have 2 equations:<BR>\n" );
document.write( "x+y = 9<BR>\n" );
document.write( "y = 2x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since y = 2x in the second equation, you substitute 2x for y in the first equation to get:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x + 2x = 9<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "3x = 9<BR>\n" );
document.write( "divide both sides by 3 to get:<BR>\n" );
document.write( "x = 9/3 = 3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since x = 3, take any equation and solve for y.<BR>\n" );
document.write( "second equation says y = 2x<BR>\n" );
document.write( "since x = 3,<BR>\n" );
document.write( "y = 2*3 = 6<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since x = 3 and y = 6, plug these values into the first equation to get:<BR>\n" );
document.write( "x + y = 9<BR>\n" );
document.write( "3 + 6 = 9<BR>\n" );
document.write( "9 = 9<BR>\n" );
document.write( "equation is true so values of x = 3 and y = 6 are good.<BR>\n" );
document.write( "graph of these equations should show the intersection of the 2 lines at the point (x,y) = (3,6)<BR>\n" );
document.write( "in order to graph these equations, make them so that y is on the left hand side of the equation and x is on the right hand side of the equation (solve for y in both equations).<BR>\n" );
document.write( "second equation is already there:<BR>\n" );
document.write( "y = 2x<BR>\n" );
document.write( "first equation needs to be manipulated:<BR>\n" );
document.write( "x + y = 9<BR>\n" );
document.write( "subtract x from both sides of the equation to get:<BR>\n" );
document.write( "y = 9-x<BR>\n" );
document.write( "first equation is now in the right form.<BR>\n" );
document.write( "both equations that are in graphing form are:<BR>\n" );
document.write( "y = 2x<BR>\n" );
document.write( "y = 9-x<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "here's a graph of the equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28800%2C800%2C-1%2C10%2C-2%2C15%2C2x%2C9-x%29 ALIGN=MIDDLE  ALT=\"graph+%28800%2C800%2C-1%2C10%2C-2%2C15%2C2x%2C9-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can see that these lines intersect at the point (3,6) which is exacty the point we calculated them to be when we solved both equations simultaneously. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );