document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=143786>Question 143786</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by setting up the proper equation to describe the facts given and then carrying out the mathematical calculations to solve for the unknown variable(s). <BR>\n" );
document.write( "The difference between two numbers is 3, and the sum of those two numbers is 21. What are the two numbers? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #104635 by </B><A HREF=/tutors/aboutme.mpl?userid=marcsam823><B>marcsam823(57)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=marcsam823><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=104635\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the first number <BR>\n" );
document.write( "Let y = the second number <BR>\n" );
document.write( "Let x + y = 21<BR>\n" );
document.write( "Let x - y = 3\r<BR>\n" );
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document.write( "I'll show you two strageties for solving this.<BR>\n" );
document.write( "1) The first is the method of addition: add the equations together to eliminate a variable.<BR>\n" );
document.write( "2) The second is the method of substitution: solve one of the equations in terms of one variable and and plug in or substitute that expression into the other equations. <BR>\n" );
document.write( "Having more than one strategy to solve a problem allows for more flexibility in your approach!\r<BR>\n" );
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document.write( "Method of addition:<BR>\n" );
document.write( "1) Add the two equations together. Note that each of the y terms cancel each other out. Combine like terms:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+21 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+y+=+3 ALIGN=MIDDLE  ALT=\"x+-+y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+=+24 ALIGN=MIDDLE  ALT=\"2x+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Divide both sides by 12\r<BR>\n" );
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document.write( "4) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+%2B+y+=+21 ALIGN=MIDDLE  ALT=\"12+%2B+y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Pick one of the given equations and solve for y by substituting your answer for x.\r<BR>\n" );
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document.write( "5) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9 ALIGN=MIDDLE  ALT=\"y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract 12 from both sides\r<BR>\n" );
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document.write( "6) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%29+-+%289%29+=+3 ALIGN=MIDDLE  ALT=\"%2812%29+-+%289%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Check your answers by substituting into the other equation.<BR>\n" );
document.write( "   <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+3 ALIGN=MIDDLE  ALT=\"3+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This checks out<BR>\n" );
document.write( "The solution is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9 ALIGN=MIDDLE  ALT=\"y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Method of substitution: <BR>\n" );
document.write( "Let x = the first number <BR>\n" );
document.write( "Let y = the second number <BR>\n" );
document.write( "Let x + y = 21<BR>\n" );
document.write( "Let x - y = 3\r<BR>\n" );
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document.write( "1) Select one of the equations and solve for one of the variables (Let's solve our second equation for x}}}\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+y+=+3 ALIGN=MIDDLE  ALT=\"x+-+y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3+%2B+y ALIGN=MIDDLE  ALT=\"x+=+3+%2B+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Add y to both sides\r<BR>\n" );
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document.write( "2) Substitute this expression for x in the other equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+21 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283+%2B+y%29+%2B+y+=+21 ALIGN=MIDDLE  ALT=\"%283+%2B+y%29+%2B+y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3) Solve for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+%2B+2y+=+21 ALIGN=MIDDLE  ALT=\"3+%2B+2y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y+=+18 ALIGN=MIDDLE  ALT=\"2y+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" >      Subtract 3 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9 ALIGN=MIDDLE  ALT=\"y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >        Divide both sides by 2\r<BR>\n" );
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document.write( "4) Substitute this solution for y and solve for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+y+=+21 ALIGN=MIDDLE  ALT=\"x+%2B+y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+9+=+21 ALIGN=MIDDLE  ALT=\"x+%2B+9+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "5) Check your answers by substituting your into the other equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+y+=+3 ALIGN=MIDDLE  ALT=\"x+-+y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%29+-+%289%29+=+3 ALIGN=MIDDLE  ALT=\"%2812%29+-+%289%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+=+3 ALIGN=MIDDLE  ALT=\"3+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "This checks out<BR>\n" );
document.write( "The solution is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+12 ALIGN=MIDDLE  ALT=\"x+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9 ALIGN=MIDDLE  ALT=\"y+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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