document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120563>Question 120563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of two numbers is 50 and their difference is 18. Find the numbers.\r<BR>\n" );
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document.write( "Im so confused could someone please help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88382 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=88382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's call one of the numbers x and the other one y.  Their sum is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By ALIGN=MIDDLE  ALT=\"x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and their difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y ALIGN=MIDDLE  ALT=\"x-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The sum of two numbers, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By ALIGN=MIDDLE  ALT=\"x%2By\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is, (=), 50, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The difference of the same two numbers, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y ALIGN=MIDDLE  ALT=\"x-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is, (=), 18, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-y=18 ALIGN=MIDDLE  ALT=\"x-y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you have a system of two equations in two variables.  There are a number of methods to solve these systems, but this one lends itself to the Gaussian Elimination method.  In this case, just add the two equations term by term which will eliminate the y variable, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   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=18 ALIGN=MIDDLE  ALT=\"x-y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Bx%2By-y=50%2B18 ALIGN=MIDDLE  ALT=\"x%2Bx%2By-y=50%2B18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B0y=68 ALIGN=MIDDLE  ALT=\"2x%2B0y=68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2F2=68%2F2 ALIGN=MIDDLE  ALT=\"2x%2F2=68%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=34 ALIGN=MIDDLE  ALT=\"x=34\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So one of the numbers has to be 34.  You can get the other just by subtracting 34 from 50 because of the relationship <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but I'm going to show the elimination method on the original two equations to eliminate the x variable this time.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   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=18 ALIGN=MIDDLE  ALT=\"x-y=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Step 1:  Multiply the bottom equation by -1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=50 ALIGN=MIDDLE  ALT=\"x%2By=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2By=-18 ALIGN=MIDDLE  ALT=\"-x%2By=-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add them term by term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-x%2By%2By=50-18 ALIGN=MIDDLE  ALT=\"x-x%2By%2By=50-18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0x%2B2y=32 ALIGN=MIDDLE  ALT=\"0x%2B2y=32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y%2F2=32%2F2 ALIGN=MIDDLE  ALT=\"2y%2F2=32%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=16 ALIGN=MIDDLE  ALT=\"y=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check your answer:\r<BR>\n" );
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document.write( "34 + 16 = 50\r<BR>\n" );
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document.write( "34 - 16 = 18.\r<BR>\n" );
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document.write( "Answer checks.\r<BR>\n" );
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document.write( "Hope this helps.<BR>\n" );
document.write( "John </SPAN>\n" );
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