document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320609>Question 320609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.Without graphing, determine whether each system has one solution, no solutions, or an infinite number of solutions.  Show your work. (2 marks each)\r<BR>\n" );
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document.write( "( a ) 4 x – y = 5	   <BR>\n" );
document.write( "      y = 4 x + 6\r<BR>\n" );
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document.write( "( b )3x + 2y = 5		<BR>\n" );
document.write( "     15x + 10y = 25\r<BR>\n" );
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document.write( "2.   How can you tell by looking at an equation whether it has one, none or infinite solutions?											 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229609 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=229609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "One question per post, please.\r<BR>\n" );
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document.write( "If you have a system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a_1x\ +\ b_1y\ =\ c_1\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a_2x\ +\ b_2y\ =\ c_2\">\r<BR>\n" );
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document.write( "and the coefficients are such that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a_1\ =\ ka_2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b_1\ =\ kb_2\">\r<BR>\n" );
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document.write( "but <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE c_1\ \neq\ kc_2\">\r<BR>\n" );
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document.write( "then you have a system that is inconsistent, i.e., has no solutions. (parallel lines)\r<BR>\n" );
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document.write( "If the coefficients are such that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a_1\ =\ ka_2\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b_1\ =\ kb_2\">\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE c_1\ =\ kc_2\">\r<BR>\n" );
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document.write( "then you have a system that is consistent and dependent, i.e. there are infinite solutions (the same line)\r<BR>\n" );
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document.write( "If the coefficients are such that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a_1\ =\ ka_2\"> but <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE b_1\ \neq\ kb_2\">,\r<BR>\n" );
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document.write( "then you have a consistent and independent system, i.e. exactly one solution (intersecting lines)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ k\ \in\ \mathbb{R}\">\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" );
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