document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118350>Question 1118350</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In this systems of equations, how can I figure out what the 2nd equation's minimum/least dollar value is?\r<BR>\n" );
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document.write( "Purchases of $6 or $4 each month. Is there a better way to solve this?<BR>\n" );
document.write( "Thanks in advance.\r<BR>\n" );
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document.write( "m+s=12\r<BR>\n" );
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document.write( "6m+4s=?<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 #733630 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=733630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ------------------------------------------------------------------------<BR>\n" );
document.write( "In this systems of equations, how can I figure out what the 2nd equation's minimum/least dollar value is?\r<BR>\n" );
document.write( "\n" );
document.write( "Purchases of $6 or $4 each month. Is there a better way to solve this?<BR>\n" );
document.write( "Thanks in advance.\r<BR>\n" );
document.write( "\n" );
document.write( "m+s=12\r<BR>\n" );
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document.write( "6m+4s=?<BR>\n" );
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document.write( "The second equation is incomplete; it is only an expression, but not an equation.  What are the variables, m and s, supposed to be?  quantity counts for $6 and $4 ?  If they are, then  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%3E=0 ALIGN=MIDDLE  ALT=\"m%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%3E=0 ALIGN=MIDDLE  ALT=\"s%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and each is only whole-numbers or 0.\r<BR>\n" );
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document.write( "If vertical axis counts m and horizontal axis counts s then graph for first equation is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-1%2C12%2C-1%2C12%2C12-x%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-1%2C12%2C-1%2C12%2C12-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "m for vertical axis and s for horizontal axis;<BR>\n" );
document.write( "counts y and counts x for m and for x, respectively.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6m%2B4s ALIGN=MIDDLE  ALT=\"6m%2B4s\"   DISABLED_style= \"max-width:90%; height:auto;\" > does not establish any constrain unless it is equated to some value.  \r<BR>\n" );
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document.write( "Are you trying to make something like   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28m%29=6m%2B4s ALIGN=MIDDLE  ALT=\"f%28m%29=6m%2B4s\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Bs=12 ALIGN=MIDDLE  ALT=\"m%2Bs=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > as a restriction?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28m%29=6m%2B4%2812-m%29 ALIGN=MIDDLE  ALT=\"f%28m%29=6m%2B4%2812-m%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28m%29=6m%2B48-4m ALIGN=MIDDLE  ALT=\"f%28m%29=6m%2B48-4m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28m%29=2m%2B48 ALIGN=MIDDLE  ALT=\"f%28m%29=2m%2B48\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdm=2 ALIGN=MIDDLE  ALT=\"df%2Fdm=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but then this is a constant, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df%2Fdm%3C%3E0 ALIGN=MIDDLE  ALT=\"df%2Fdm%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "No minimum for f and no maximum for f.\r<BR>\n" );
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document.write( "The SMALLEST value that m can be is  0, and this will make  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28f%28m%29=f%280%29=2%2A0%2B48=highlight%2848%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28f%28m%29=f%280%29=2%2A0%2B48=highlight%2848%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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