document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237908>Question 237908</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a linear system as a model of the following situation, then solve.<BR>\n" );
document.write( "Your school's star basketball player was excited about his play during the last game. He remembered that he scored 3-point shots, but couldn't recall how many free throws (worth 1 point each) and field goals (worth 2 points each) he scored. The scorekeeper said he had scored 20 times for 34 points.<BR>\n" );
document.write( "How many field goals did he make? How many free throws did he make?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174882 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=174882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "If you meant to say that he scored <i>three</i> 3-point shots, then it works out this way.\r<BR>\n" );
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document.write( "Three 3-point shots is 3 shots worth 9 points, so the field goals and free throws have to account for 17 of the 20 shots and 25 of the 34 points.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the number of field goals and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> the number of free throws.  Then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x\"> is the number of field goal points and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\"> is the number of free throw points.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \ x\ +\ y\ =\ 17\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2x\ +\ y\ =\ 25\">\r<BR>\n" );
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document.write( "Multiply the first equation by -1:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -x\ -\ y\ =\ -17\">\r<BR>\n" );
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document.write( "Add this new equation to the original 2nd equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ 0y\ =\ 8\">\r<BR>\n" );
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document.write( "So, 8 field goals, and 17 - 8 = 9 free throws.\r<BR>\n" );
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document.write( "Check:  3 three-pointers for 9 points, 8 field goals for 16 points, and 9 free throws for 9 points.  3 + 8 + 9 = 20 and 9 + 16 + 9 = 34.  Checks.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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