document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=641139>Question 641139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of a certain number and a second number is -42. the first number minus the second is 52. find the numbers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403545 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><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=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=403545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To solve, let's turn each of the sentences into an equation.  The first sentence says that the sum of a certain number and a second number is -42.  In other words:\r<BR>\n" );
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document.write( "x + y = -42 (where x and y each represent one of those numbers)\r<BR>\n" );
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document.write( "The second sentence says that the first number minus the second number is 52.  In other words:\r<BR>\n" );
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document.write( "x - y = 52\r<BR>\n" );
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document.write( "These two equations form a system of linear equations.  We can find x and y by adding these two equations together.  So,\r<BR>\n" );
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document.write( "x + y + x - y = -42 + 52\r<BR>\n" );
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document.write( "Leaving us with\r<BR>\n" );
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document.write( "2x = 10\r<BR>\n" );
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document.write( "Dividing both sides by 2 will leave us with x:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F2=10%2F2 ALIGN=MIDDLE  ALT=\"2x%2F2=10%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "x = 5\r<BR>\n" );
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document.write( "Now, to solve for y, just replace x in either equation, with 5.  Let's use the first equation:  x + y = -42:\r<BR>\n" );
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document.write( "5 + y = -42\r<BR>\n" );
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document.write( "Subtract both sides by 5:\r<BR>\n" );
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document.write( "5 - 5 + y = -42 - 5, so\r<BR>\n" );
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document.write( "y = -47\r<BR>\n" );
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document.write( "FINAL ANSWER: 5 and -47 are the two numbers </SPAN>\n" );
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