document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181775>Question 181775</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if (2a + b = 80) and (2b + a = 76) then a = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136372 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=136372\">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( "You can do this either by substitution or elimination.\r<BR>\n" );
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document.write( "<i><b><u>Substitution</u></b></i>\r<BR>\n" );
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document.write( "Step 1: Solve the first equation for <i>b</i>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2a + b = 80\ \ \Rightarrow\ \ b = 80 - 2a\">\r<BR>\n" );
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document.write( "Step 2: Substitute the expression in <i>a</i> for <i>b</i> in the 2nd equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2b + a = 76 \ \ \Rightarrow\ \ 2(80 - 2a) + a = 76\">\r<BR>\n" );
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document.write( "Step 3: Solve this new equation for <i>a</i>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2(80 - 2a) + a = 76\ \ \Rightarrow\ \ 160 - 4a + a = 76\ \ \Rightarrow\ \ 160 - 3a = 76 \cr \text{          }\math \ \ \Rightarrow\ \ -3a = 76 - 160\ \ \Rightarrow\ \ -3a = -84\ \ \Rightarrow\ \ a = 28\">\r<BR>\n" );
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document.write( "From here you could substitute 28 for <i>a</i> in either of the original equations and then solve for <i>b</i> if you needed to.\r<BR>\n" );
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document.write( "<i><b><u>Elimination</u></b></i>\r<BR>\n" );
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document.write( "Step 1:  Rearrange the equations so that the variables are in the same order:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2b + a = 76\ \ \Rightarrow\ \ a + 2b = 76\">\r<BR>\n" );
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document.write( "Step 2:  Multiply the 1st equation by -2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math 2a + b = 80\ \ \Rightarrow\ \ -4a - 2b = - 160\">\r<BR>\n" );
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document.write( "Step 3:  Add this new form of  1st equation to the 2nd equation term by term and solve for <i>a</i>:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math (-4a - 2b ) + (a + 2b) = (-160)+(76) \ \ \Rightarrow\ \ (- 4a + a) + (-2b + 2b) = -84\cr  \text{          }\math\ \ \Rightarrow\ \ -3a = -84 \ \ \Rightarrow\ \ a = 28\">\r<BR>\n" );
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document.write( "Same result.\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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