document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=247831>Question 247831</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to show this problem can be solved by substitution, can you please help me?  -4x + 2y = 16 and 3x -y = 2 These are systems of linear equations </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180667 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=180667\">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( "To solve by substitution, solve either one of your equations for one of the variables in terms of the other.  This will give you an expression that can be substituted in the other equation.  Mathematically, it doesn't matter which equation you choose or which variable you choose -- it all comes out to the same thing in the end given correctly performed arithmetic.  However, sometimes it is easier to manipulate one way than another.  Your problem is like this.\r<BR>\n" );
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document.write( "Compare all of your coefficients.  If you try to solve either of your equations for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, you will either have to divide by 4 or by 3.  Either way, somewhere you will end up with a fraction to deal with.  On the other hand, solving for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> means that you will have to divide by 2 or -1, and that means no fractions.\r<BR>\n" );
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document.write( "Let's solve the second equation for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x\ -\ y\ =\ 2\">\r<BR>\n" );
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document.write( "Add -3x to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -\ y\ =\ -3x\ +\ 2\">\r<BR>\n" );
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document.write( "Multiply both sides by -1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ 3x\ -\ 2\">\r<BR>\n" );
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document.write( "Now you have something in terms of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> that you can substitute for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> in your other equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -4x\ +\ 2y\ =\ 16\">\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -4x\ +\ 2\left(3x\ -\ 2\right)\ =\ 16\">\r<BR>\n" );
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document.write( "Which is a single equation in a single variable that can be solved by ordinary means.  Once you have solved for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">, you can use that value to substitute into either equation and then solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">.  Write back and let me know what you obtained for a solution set for this system.\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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