document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=253004>Question 253004</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If x^2 - y^2 = 28 and x - y = 8 what is the average of x and y?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #185200 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=185200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 - y^2 = 28 (first equation)<BR>\n" );
document.write( "x - y = 8 (second equation)\r<BR>\n" );
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document.write( "solve for x in second equation to get:\r<BR>\n" );
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document.write( "x = y+8\r<BR>\n" );
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document.write( "substitute for x in first equation to get:\r<BR>\n" );
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document.write( "x^2 - y^2 = 28 becomes:\r<BR>\n" );
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document.write( "(y+8)^2 - y^2 = 28\r<BR>\n" );
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document.write( "simplify by performing indicated operations to get:\r<BR>\n" );
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document.write( "y^2 + 16y + 64 - y^2 = 28\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "16y + 64 = 28\r<BR>\n" );
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document.write( "subtract 64 from both sides to get:\r<BR>\n" );
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document.write( "16y = 28-64 = -36\r<BR>\n" );
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document.write( "divide both sides by 16 to get:\r<BR>\n" );
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document.write( "y = -36/16\r<BR>\n" );
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document.write( "substitute in second equation to get:\r<BR>\n" );
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document.write( "x - y = 8 becomes:\r<BR>\n" );
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document.write( "x - (-36/16) = 8.\r<BR>\n" );
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document.write( "simplify by performing indicated operations to get:\r<BR>\n" );
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document.write( "x + 36/16 = 8\r<BR>\n" );
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document.write( "subtract 36/16 from both sides to get:\r<BR>\n" );
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document.write( "x = 8 - 36/16 = 128/16 - 36/16 = 92/16.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 92/16<BR>\n" );
document.write( "y = -36/16\r<BR>\n" );
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document.write( "substitute in first equation to get:\r<BR>\n" );
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document.write( "x^2 - y^2 = 28 becomes:\r<BR>\n" );
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document.write( "(92/16)^2 - (-36/16)^2 = 28\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "33.0625 - 5.0625 = 28 confirming that the values for x and y are good.\r<BR>\n" );
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document.write( "the question was:\r<BR>\n" );
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document.write( "what is the average of x and y?\r<BR>\n" );
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document.write( "the average of x and y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2892%2F16%29+%2B+%28-36%2F16%29%29%2F2+=+%28%2892%2F16%29+-+%2836%2F16%29%29%2F2+=+%2856%2F16%29%2F2+=+%2856%2F32%29+=+1.75 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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