document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146202>Question 146202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hockey teams receive 2 points when they win and 1 point when they tie.  One season, a team won a championship with 57 points.  They won 9 more games than they tied.  How many wins and how many ties did the team have? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106755 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=106755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let w=# of wins, and t=# of ties\r<BR>\n" );
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document.write( "The sentences \"Hockey teams receive 2 points when they win and 1 point when they tie.  One season, a team won a championship with 57 point\" translate to the first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%2Bt=57 ALIGN=MIDDLE  ALT=\"2w%2Bt=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And the sentence \"They won 9 more games than they tied\" translates to the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=t%2B9 ALIGN=MIDDLE  ALT=\"w=t%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Start with the given system\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%2Bt=57 ALIGN=MIDDLE  ALT=\"2w%2Bt=57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=t%2B9 ALIGN=MIDDLE  ALT=\"w=t%2B9\"   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=2%28t%2B9%29%2Bt=57 ALIGN=MIDDLE  ALT=\"2%28t%2B9%29%2Bt=57\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=t%2B9 ALIGN=MIDDLE  ALT=\"w=t%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the first equation. In other words, replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2B9 ALIGN=MIDDLE  ALT=\"t%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Notice we've eliminated the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" > variables. So we now have a simple equation with one unknown.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%2B18%2Bt=57 ALIGN=MIDDLE  ALT=\"2t%2B18%2Bt=57\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3t%2B18=57 ALIGN=MIDDLE  ALT=\"3t%2B18=57\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3t=57-18 ALIGN=MIDDLE  ALT=\"3t=57-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >Subtract 18 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3t=39 ALIGN=MIDDLE  ALT=\"3t=39\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%2839%29%2F%283%29 ALIGN=MIDDLE  ALT=\"t=%2839%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to isolate t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=13 ALIGN=MIDDLE  ALT=\"t=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "Now that we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=13 ALIGN=MIDDLE  ALT=\"t=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can plug this into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=t%2B9 ALIGN=MIDDLE  ALT=\"w=t%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   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=w=%2813%29%2B9 ALIGN=MIDDLE  ALT=\"w=%2813%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > for each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   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=w=22 ALIGN=MIDDLE  ALT=\"w=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=22 ALIGN=MIDDLE  ALT=\"w=22\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=13 ALIGN=MIDDLE  ALT=\"t=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the team won 22 games and tied 13 games\r<BR>\n" );
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document.write( " </SPAN>\n" );
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