document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255923>Question 255923</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of two numbers is 13. two times the first number minus three times the second number is 1. if you let x stand for the first number and y for the second number, what are the two numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188289 by </B><A HREF=/tutors/aboutme.mpl?userid=EMStelley><B>EMStelley(208)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EMStelley><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=EMStelley><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=188289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If our two numbers are x and y, to do this problem we just take it one sentence at a time.\r<BR>\n" );
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document.write( "\"the sum of two numbers is 13\"<BR>\n" );
document.write( "This tells us that when you add our two numbers you get 13.  So we have:<BR>\n" );
document.write( "x+y=13\r<BR>\n" );
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document.write( "\"two times the first number minus three times the second number is 1\"<BR>\n" );
document.write( "Two times the first number would be represented by 2x and three times the second number is represented by 3y.  So we have:<BR>\n" );
document.write( "2x-3y=1\r<BR>\n" );
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document.write( "So we have a system of equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=13 ALIGN=MIDDLE  ALT=\"x%2By=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=1 ALIGN=MIDDLE  ALT=\"2x-3y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the addition method to solve this system.  If we multiply the first equation by 3 we will be able to eliminate the y's.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2B3y=39 ALIGN=MIDDLE  ALT=\"3x%2B3y=39\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-3y=1 ALIGN=MIDDLE  ALT=\"2x-3y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we add:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x=40 ALIGN=MIDDLE  ALT=\"5x=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=8 ALIGN=MIDDLE  ALT=\"x=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And using our first equation we have that y must be 5.  So our two numbers are 8 and 5. </SPAN>\n" );
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