document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622413>Question 622413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five times a number plus four times a second number equal to eighty-three. The difference between the two numbers is 5. Find 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 #391372 by </B><A HREF=/tutors/aboutme.mpl?userid=matineesuxxx><B>matineesuxxx(27)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=matineesuxxx><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=391372\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x represent the smaller number,<BR>\n" );
document.write( "let y represent the larger number\r<BR>\n" );
document.write( "\n" );
document.write( "therefore,<BR>\n" );
document.write( "\"five times a number plus four times a second number is 83\"<BR>\n" );
document.write( "that means, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B4y=83 ALIGN=MIDDLE  ALT=\"5x%2B4y=83\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and if, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x=5 ALIGN=MIDDLE  ALT=\"y-x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=5%2Bx ALIGN=MIDDLE  ALT=\"y=5%2Bx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "therefore, since we now know what y equals, plug it back into the equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B4%285%2Bx%29=83 ALIGN=MIDDLE  ALT=\"5x%2B4%285%2Bx%29=83\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B20%2B4x=83 ALIGN=MIDDLE  ALT=\"5x%2B20%2B4x=83\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%2B20=83 ALIGN=MIDDLE  ALT=\"9x%2B20=83\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x=63 ALIGN=MIDDLE  ALT=\"9x=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=63%2F9 ALIGN=MIDDLE  ALT=\"x=63%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7 ALIGN=MIDDLE  ALT=\"x=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now plug that x value into the equation, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x=5 ALIGN=MIDDLE  ALT=\"y-x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that you have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-7=5 ALIGN=MIDDLE  ALT=\"y-7=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12 ALIGN=MIDDLE  ALT=\"y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "NOW you can also solve this by using a system of equations.<BR>\n" );
document.write( "the first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B5x=83 ALIGN=MIDDLE  ALT=\"4y%2B5x=83\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the second is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x=5 ALIGN=MIDDLE  ALT=\"y-x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "place one on top of the other \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B5x=83 ALIGN=MIDDLE  ALT=\"4y%2B5x=83\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x=5 ALIGN=MIDDLE  ALT=\"y-x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "now notice if you multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-x=5 ALIGN=MIDDLE  ALT=\"y-x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > by positive 5 and add the two equations, you will be able to eliminate the x.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y%2B5x=83 ALIGN=MIDDLE  ALT=\"4y%2B5x=83\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5y-5x=25 ALIGN=MIDDLE  ALT=\"5y-5x=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9y=108 ALIGN=MIDDLE  ALT=\"9y=108\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=12 ALIGN=MIDDLE  ALT=\"y=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > and now once again plug y in and solve for x and you get 7. </SPAN>\n" );
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