document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=103927>Question 103927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you're solving a system of two linear equations and you arrive at an equation 0 = 0. (What an astounding fact!) What does that tell you about the relationship of the two lines? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #75608 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=75608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say you have the two equations <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B1 ALIGN=MIDDLE  ALT=\"y=2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=4x%2B2 ALIGN=MIDDLE  ALT=\"2y=4x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If you divide both sides of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=4x%2B2 ALIGN=MIDDLE  ALT=\"2y=4x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 2 you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B1 ALIGN=MIDDLE  ALT=\"y=2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (which is the same equation as the first one)\r<BR>\n" );
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document.write( "Now set the two equations equal to each other\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B1-2x=1 ALIGN=MIDDLE  ALT=\"2x%2B1-2x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-2x=1-1 ALIGN=MIDDLE  ALT=\"2x-2x=1-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1 from both sides\r<BR>\n" );
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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;\" > Subtract\r<BR>\n" );
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document.write( "So if you set one side of an equation equal to itself, then you get the identity <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;\" >. This means that any x value will satisfy the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%2B1 ALIGN=MIDDLE  ALT=\"y=2x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So there are an infinite number of solutions and the system is dependent (since the second equation is dependent on the first one) </SPAN>\n" );
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