document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=545941>Question 545941</A>: <I><SPAN STYLE=\"word-break: break-all;\"> without graphing answer the following questions about the system, x-y=7, <BR>\n" );
document.write( "9x=9y+4.\r<BR>\n" );
document.write( "\n" );
document.write( "Does this system have a solution?<BR>\n" );
document.write( "yes or no?\r<BR>\n" );
document.write( "\n" );
document.write( "Is the system inconsistent, are the equations dependent, or neither?\r<BR>\n" );
document.write( "\n" );
document.write( "What does this graph look like? Intersecting lines? One line? Or parallel lines?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you for your help<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 #355793 by </B><A HREF=/tutors/aboutme.mpl?userid=lmeeks54><B>lmeeks54(111)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lmeeks54><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=lmeeks54><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=355793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have two equations in your system:<BR>\n" );
document.write( "...<BR>\n" );
document.write( "x - y = 7<BR>\n" );
document.write( "9x = 9y + 4<BR>\n" );
document.write( "...<BR>\n" );
document.write( "since these both describe straight lines, it is useful to convert them into standard slope-intercept form: y = mx + b:<BR>\n" );
document.write( "...<BR>\n" );
document.write( "x - y = 7<BR>\n" );
document.write( "y = x - 7<BR>\n" );
document.write( "...<BR>\n" );
document.write( "9x = 9y + 4<BR>\n" );
document.write( "y = x - 4/9<BR>\n" );
document.write( "...<BR>\n" );
document.write( "in both, the slopes are m = 1; however, the y intercepts are different:<BR>\n" );
document.write( "1st eqn: b = -7<BR>\n" );
document.write( "2nd eqn: b = -4/9<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Is there a solution to this system?  No, there is no common point which solves both equations.  This is also the meaning of an inconsistent system of linear equations: there is no solution to the system.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "The graph would like two parallel lines with positive slope upwards to the right.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "cheers,<BR>\n" );
document.write( "Lee </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );