document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=247206>Question 247206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have already passed algebra but didn't pass the EOC and have forgotten alot of information. But anyway one of my questions is using substituion and elimination.   x-11y=-123  11x-y=-33  i forget where and how to start. could you please help me?? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180387 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=180387\">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( "<b>Substitution Method:</b>  Solve one of your equations for one of the variables in terms of the other, then substitute the expression for the chosen variable into the second equation.  Thus:\r<BR>\n" );
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document.write( "Equation 1:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 11y\ =\ -123\">\r<BR>\n" );
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document.write( "Equation 2:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 11x\ -\ y\ =\ -33\">\r<BR>\n" );
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document.write( "Add 11y to both sides of Equation 1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ =\ 11y\ -\ 123\">\r<BR>\n" );
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document.write( "Substitute into Equation 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 11\left(11y\ -\ 123\right)\ -\ y\ =\ -33\">\r<BR>\n" );
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document.write( "Now just simplify and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">.  Once you have the value of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">, substitute that back into either equation and solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">.\r<BR>\n" );
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document.write( "<b>Elimination Method:</b>  Multiply one or both equations by some value that makes the coefficient on one of the variables equal to the additive inverse of that same variable's coefficient in the other equation.  Then add the equations term-by-term.  The coefficient of the chosen variable in the sum will be zero, eliminating (hence the name of the method) that variable and leaving you with a single equation in a single variable that can be solved by ordinary means. Thus:\r<BR>\n" );
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document.write( "Equation 1:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 11y\ =\ -123\">\r<BR>\n" );
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document.write( "Equation 2:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 11x\ -\ y\ =\ -33\">\r<BR>\n" );
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document.write( "Multiply Equation 2 by -11:\r<BR>\n" );
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document.write( "Equation 3:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -121x\ +\ 11y\ =\ 363\">\r<BR>\n" );
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document.write( "Add Equation 3 to Equation 1, term-by-term:\r<BR>\n" );
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document.write( "Equation 4:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -120x\ +\ 0y\ =\ 240\">\r<BR>\n" );
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document.write( "Notice that the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> term has been eliminated.\r<BR>\n" );
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document.write( "Now all you have to do is solve:\r<BR>\n" );
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document.write( "Equation 4:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -120x\ =\ 240\">\r<BR>\n" );
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document.write( "And then substitute the calculated value for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> back into either of the original equations and solve the result for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\">.\r<BR>\n" );
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document.write( "Let me know what you come up with.\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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