document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462157>Question 462157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> James scored 19 times during one basketball. He scored a total of 28 points, two for each field goal and one for each free-throw. How many field goals did he make? How many free-throws?<BR>\n" );
document.write( " a) define one variable for the number of field goals made. another variable for the free-throws.<BR>\n" );
document.write( " b) write an expression that represents the total points made from field goals. another one for free-throws.<BR>\n" );
document.write( " c) write an equation that describes the number of times that James scored during the game. write an equation for the total score.<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 #316881 by </B><A HREF=/tutors/aboutme.mpl?userid=graphmatics><B>graphmatics(170)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=graphmatics><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=graphmatics><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Let x be the number of field goals and y be the number of free-throws.\r<BR>\n" );
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document.write( "b) The total points from field goals is 2*x.<BR>\n" );
document.write( "   The total points from free-throws is y<BR>\n" );
document.write( "c) The number of times that James scored during the game is x+y = 19.<BR>\n" );
document.write( "   Because he scored a total of 28 points 2*x+y = 28<BR>\n" );
document.write( "So we will need to solve the linear system of equations<BR>\n" );
document.write( "x+y = 19<BR>\n" );
document.write( "2*x+y = 28\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear.solver>Linear System solver (using determinant)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+19%2C%0D%0A++++2%5Cx+%2B+1%5Cy+=+28+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+19%2C%0D%0A++++2%5Cx+%2B+1%5Cy+=+28+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2Ax+%2B+a%5B12%5D%2Ay+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Ax+%2B+a%5B22%5D%2Ay+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++x+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++y+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++++x+=+%2819%2A1+-+28%2A1%29%2F%281%2A1-2%2A1%29+=+9%2C%0D%0A++++++y+=+%281%2A28+-+2%2A19%29%2F%281%2A1-2%2A1%29+=+10%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (x=9, y=10}<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " </SPAN>\n" );
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