document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=278248>Question 278248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4x-2y=4<BR>\n" );
document.write( "-20x+10y=-20\r<BR>\n" );
document.write( "\n" );
document.write( "is there no solution and does the graph only intersect at 1 point so the solution is unique? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202489 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=202489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
document.write( "\n" );
document.write( "Start with the given system of equations:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%284x-2y=4%2C-20x%2B10y=-20%29 ALIGN=MIDDLE  ALT=\"system%284x-2y=4%2C-20x%2B10y=-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%284x-2y%29=5%284%29 ALIGN=MIDDLE  ALT=\"5%284x-2y%29=5%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x-10y=20 ALIGN=MIDDLE  ALT=\"20x-10y=20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we have the new system of equations:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2820x-10y=20%2C-20x%2B10y=-20%29 ALIGN=MIDDLE  ALT=\"system%2820x-10y=20%2C-20x%2B10y=-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x-10y%29%2B%28-20x%2B10y%29=%2820%29%2B%28-20%29 ALIGN=MIDDLE  ALT=\"%2820x-10y%29%2B%28-20x%2B10y%29=%2820%29%2B%28-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x%2B-20x%29%2B%28-10y%2B10y%29=20%2B-20 ALIGN=MIDDLE  ALT=\"%2820x%2B-20x%29%2B%28-10y%2B10y%29=20%2B-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B0y=0 ALIGN=MIDDLE  ALT=\"0x%2B0y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Simplify.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=0 ALIGN=MIDDLE  ALT=\"0=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <font size=\"4\"><b>always</b></font> true, this means that there are an infinite number of solutions. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the system is consistent and dependent.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );