document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=420948>Question 420948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (5,1); 9X+y=46<BR>\n" );
document.write( "18x+2Y+92<BR>\n" );
document.write( "give order pair a solution of the system of equations. Use alphabetical order is it in order pair solution? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #294009 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=294009\">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( "No!  Not alphabetical.\r<BR>\n" );
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document.write( "The first element of an ordered pair is the value of the independent variable, and the second is the dependent variable.  Generally and typically, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> is the independent variable and is plotted on the horizontal axis.  While <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> is the dependent or function value variable and is plotted on the vertical axis.  The fact that these two alphabetic characters happen to be listed in alphabetical order in the ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x,y)\"> is nothing but coincidence.\r<BR>\n" );
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document.write( "The problem arises when you have a 2 by 2 system of equations where the given variables are not <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">.  Then how do you identify which is the independent variable and which is the function value variable?  I suspect that your text/teacher/instructor/professor has made the convention that, for the purposes of this course, the order of variables in the sense of an ordered pair will, in fact and indeed, be alphabetical.\r<BR>\n" );
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document.write( "By the way, the example you gave has four different variables, not two.  X is NOT the same as x, and Y is NOT the same as y.  Furthermore, you only have one equation since there is no equals sign in your second expression.\r<BR>\n" );
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document.write( "Now, if what you meant was:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9x\ +\ y\ =\ 46\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 18x\ +\ 2y\ =\ 92\">\r<BR>\n" );
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document.write( "Then solve by elimination.\r<BR>\n" );
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document.write( "Multiply the first equation by -2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -18x\ -\ 2y\ =\ -92\">\r<BR>\n" );
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document.write( "Add the two equations term by term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 0\ +\ 0\ =\ 0\">\r<BR>\n" );
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document.write( "Such a triviality leads to the conclusion that the two equations have the exact same solution set.  That means that any ordered pair that satisfies one of the equations will satisfy the other as well, hence the solution set of the <i><b>system</b></i> has an infinite number of elements.  The system is said to be consistent (because it has at least one solution) and dependent (because it has infinite solutions).  Graphically, these two equations represent the same line.\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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