document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=531618>Question 531618</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HOw can you tell which type system you have by looking at just the two linear equations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #350532 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=350532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Given the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \alpha_1x\ +\ \beta_1y\ =\ \gamma_1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \alpha_2x\ +\ \beta_2y\ =\ \gamma_2\">\r<BR>\n" );
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document.write( "If \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \exists\ k\ | \alpha_1\ =\ {k}\alpha_2\text{ and }\beta_1\ =\ {k}\beta_2\text{ but }\gamma_1\ \neq\ {k}\gamma_2\">\r<BR>\n" );
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document.write( "then the system is inconsistent.\r<BR>\n" );
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document.write( "If \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \exists\ k\ | \alpha_1\ =\ {k}\alpha_2\text{ and }\beta_1\ =\ {k}\beta_2\text{ and }\gamma_1\ =\ {k}\gamma_2\">\r<BR>\n" );
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document.write( "then the system is consistent and dependent.\r<BR>\n" );
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document.write( "If\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \not\exists\ k\ | \alpha_1\ =\ {k}\alpha_2\text{ and }\beta_1\ =\ {k}\beta_2\">\r<BR>\n" );
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document.write( "then the system is consistent and independent.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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