document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=27856>Question 27856</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following describes the graph of the solutions to the system <BR>\n" );
document.write( "{ 2x-4y=-1<BR>\n" );
document.write( "  x-2y=2\r<BR>\n" );
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document.write( "I dont know if its two parallel lines, no solutions OR one line, infinately many solutions? \r<BR>\n" );
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document.write( "Thanks a bunch!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15173 by </B><A HREF=/tutors/aboutme.mpl?userid=bmauger><B>bmauger(101)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bmauger><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=15173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4y=-1 ALIGN=MIDDLE  ALT=\"2x-4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=2 ALIGN=MIDDLE  ALT=\"x-2y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve the second equation for x to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2B2y ALIGN=MIDDLE  ALT=\"x=2%2B2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute it into the first equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4y=-1 ALIGN=MIDDLE  ALT=\"2x-4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%282%2B2y%29-4y=-1 ALIGN=MIDDLE  ALT=\"2%282%2B2y%29-4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B4y-4y=-1 ALIGN=MIDDLE  ALT=\"4%2B4y-4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%3C%3E-1 ALIGN=MIDDLE  ALT=\"4%3C%3E-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since 4 does not equal -1 there are no solutions. Meaning when you graph the equations you'll get two parallel lines.<BR>\n" );
document.write( "If we put them in slope-intercept form...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-4y=-1 ALIGN=MIDDLE  ALT=\"2x-4y=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >Rearrange to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4y=-2x-1 ALIGN=MIDDLE  ALT=\"-4y=-2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2F2-1%2F4 ALIGN=MIDDLE  ALT=\"y=x%2F2-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2y=2 ALIGN=MIDDLE  ALT=\"x-2y=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=-x%2B2 ALIGN=MIDDLE  ALT=\"-2y=-x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2F2-1 ALIGN=MIDDLE  ALT=\"y=x%2F2-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So you have two lines with slope 1/2 one with an intercept -1/4 the other with an intercept of -1. Graphically:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C+300%2C+-4%2C+4%2C+-4%2C+4%2C%0D%0A-x%2F2-1%2C%0D%0A-x%2F2-1%2F4%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C+300%2C+-4%2C+4%2C+-4%2C+4%2C%0D%0A-x%2F2-1%2C%0D%0A-x%2F2-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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