document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246>Question 246</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two numbers whose sum is 64 and whose difference is 42. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #115 by </B><A HREF=/tutors/aboutme.mpl?userid=terrtwo><B>terrtwo(10)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=terrtwo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=115\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers can be expressed algebraicly as the sum of two variables:\r<BR>\n" );
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document.write( "x + y = 64 (equation #1)\r<BR>\n" );
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document.write( "The difference of the same two numbers is expressed in like fashion:\r<BR>\n" );
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document.write( "x - y = 42  (equation #2)\r<BR>\n" );
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document.write( "We can solve this by substitution by solving the first equation for x;\r<BR>\n" );
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document.write( "x + y = 64<BR>\n" );
document.write( "--> x + y - y = 64 - y<BR>\n" );
document.write( "--> x = 64 - y\r<BR>\n" );
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document.write( "We then replace the x in the second equation with (64-y):<BR>\n" );
document.write( "x - y = 42<BR>\n" );
document.write( "--> (64 - y) - y = 42<BR>\n" );
document.write( "--> 64 -y - y = 42<BR>\n" );
document.write( "--> 64 -2y = 42\r<BR>\n" );
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document.write( "We then add 2y to both sides:\r<BR>\n" );
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document.write( "--> 64 -2y + 2y = 42 + 2y<BR>\n" );
document.write( "--> 64 = 42 + 2y\r<BR>\n" );
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document.write( "Then we subtract 42 from both sides:<BR>\n" );
document.write( "--> 64 - 42 = 42 + 2y -42<BR>\n" );
document.write( "--> 22 = 2y\r<BR>\n" );
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document.write( "Divide both sides by 2:<BR>\n" );
document.write( "--> 22/2 = 2y/2<BR>\n" );
document.write( "--> 11 = y\r<BR>\n" );
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document.write( "Then we go back and replace y in the first equation with 11:<BR>\n" );
document.write( "x + y = 64<BR>\n" );
document.write( "--> x + 11 = 64\r<BR>\n" );
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document.write( "Subtract 11 from both sides of the equation:\r<BR>\n" );
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document.write( "x + 11 -11 = 64 -11<BR>\n" );
document.write( "--> x = 53\r<BR>\n" );
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document.write( "ANSWER: the two numbers are 53 and 11\r<BR>\n" );
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document.write( " </SPAN>\n" );
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