document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68590>Question 68590</A>: <I><SPAN STYLE=\"word-break: break-all;\"> solve each of the following systems by graphing...<BR>\n" );
document.write( "2x -y = 4, 2x -y = 6  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48818 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=48818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> solve each of the following systems by graphing...<BR>\n" );
document.write( "2x -y = 4, 2x -y = 6 <BR>\n" );
document.write( "Notice that the coefficients of x and y are exactly the same, but the constant is different?  That means that the two lines are parallel and will never intersect, therefore this system has no solution.<BR>\n" );
document.write( "However, for giggles, let's graph the two lines anyway...<BR>\n" );
document.write( "For 2x-y=4<BR>\n" );
document.write( "Let x=0 and solve for y,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280%29-y=4 ALIGN=MIDDLE  ALT=\"2%280%29-y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0-y=4 ALIGN=MIDDLE  ALT=\"0-y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%2F-1=4%2F-1 ALIGN=MIDDLE  ALT=\"-y%2F-1=4%2F-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=-4 ALIGN=MIDDLE  ALT=\"y=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plot (0,-4)<BR>\n" );
document.write( "Now let y=0 and solve for x,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-0=4 ALIGN=MIDDLE  ALT=\"2x-0=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F2=4%2F2 ALIGN=MIDDLE  ALT=\"2x%2F2=4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plot (2,0)<BR>\n" );
document.write( "Connect the points and you have a line:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C2x-4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C2x-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For 2x-y=6<BR>\n" );
document.write( "Let x=0 and solve for y<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%280%29-y=6 ALIGN=MIDDLE  ALT=\"2%280%29-y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0-y=6 ALIGN=MIDDLE  ALT=\"0-y=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%2F-1=6%2F-1 ALIGN=MIDDLE  ALT=\"-y%2F-1=6%2F-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=-6 ALIGN=MIDDLE  ALT=\"y=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plot (0,-6)<BR>\n" );
document.write( "Now let y=0 and solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-0=6 ALIGN=MIDDLE  ALT=\"2x-0=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F2=6%2F2 ALIGN=MIDDLE  ALT=\"2x%2F2=6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plot (3,0)<BR>\n" );
document.write( "Connect the two points and you have another line:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C2x-4%2C2x-6%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C2x-4%2C2x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The lines are parallel, never intersect, and never have a solution.<BR>\n" );
document.write( "Happy Calculating!!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );