document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=528174>Question 528174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve/understand the system of equations by substitution? Thanks!\r<BR>\n" );
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document.write( "32x-4y=20<BR>\n" );
document.write( "y=8x+5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #349175 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=349175\">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( "If two things are equal to each other, then you can substitute one for the other any time you like.\r<BR>\n" );
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document.write( "Your second equation sets <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> equal to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 8x\ +\ 5\">\r<BR>\n" );
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document.write( "So you can substitute the expression <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 8x\ +\ 5\"> for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> whereever it is convenient to do so -- at least within the context of this problem.\r<BR>\n" );
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document.write( "That means that you can re-write your first equation thusly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x\ -\ 4(8x\ +\ 5)\ =\ 20\">\r<BR>\n" );
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document.write( "resulting in an equation in a single variable that can be solved by ordinary means.  Once you have determined the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, that value can be substituted back into either equation so as to be able to calculate the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">.\r<BR>\n" );
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document.write( "Now that you have a value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> and a value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">, you can create an ordered pair <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x,\,y\right)\"> which is the single element of the solution set of the 2X2 <i><b>system</b></i> of  equations.\r<BR>\n" );
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document.write( "If you have already done all of that and are bothered by the fact that the values of <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\"> are rather ugly fractions, remember that no one has ever given you a written guarantee that the answers to math problems would always turn out to be nice neat round numbers or fractions with single digit denominators.\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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