document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=349454>Question 349454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is there a difference between solving a system of equations by the algebraic method and the graphical method? Why or why not? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #249834 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=249834\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the graph will give you an approximate solution.\r<BR>\n" );
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document.write( "the algebra will give you an exact solution.\r<BR>\n" );
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document.write( "the reason for this is that the accuracy of the graph is not sufficient to home in on the exact solution.\r<BR>\n" );
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document.write( "an example:\r<BR>\n" );
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document.write( "x^2 + y^2 = 64<BR>\n" );
document.write( "y = 4\r<BR>\n" );
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document.write( "solve this algebraically and you will see that the solution is:\r<BR>\n" );
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document.write( "x = +/- 6.92820323\r<BR>\n" );
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document.write( "solve this graphically and you will see that the solution lies somewhere around that value, but there's no way you can get it right on unless you zero in to a very minute detail which is not possible with most graphing software that might be available to you.\r<BR>\n" );
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document.write( "the exact solution is subject to the vagaries of the accuracy of the graphing software that you use.\r<BR>\n" );
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document.write( "here's the solution on the algebra.com graphing software.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C4%2Csqrt%2864-x%5E2%29%2C-sqrt%2864-x%5E2%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C4%2Csqrt%2864-x%5E2%29%2C-sqrt%2864-x%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "you can see that the points of intersection are somewhere around x = +/- 7 but there's no way you can see that the actual solution is +/- 6.92820323.\r<BR>\n" );
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document.write( "The graphing solution is good to give you a general idea of where your solution lies, or if you even have a solution.\r<BR>\n" );
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document.write( "To get the exact solution, you need to go to the algebraic solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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