document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=440130>Question 440130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mari and James are friends.  The difference between 9 times James' age and 4 times Mari's age is 72.  Twelve years ago, James was half as old as Mari was.\r<BR>\n" );
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document.write( "a) Write a linear system to describe the relationship between Mari's age and James age.<BR>\n" );
document.write( "b)  Graph the system on a grid<BR>\n" );
document.write( "c) Five years from now, how old will Mari and James be?\r<BR>\n" );
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document.write( "I'm getting stumped on A&B.  I thought that a) would be 9x-4y=72, and b) would be j-12=1/2(y-12), but the two aren't intersecting, so I must be thinking the equation incorrectly! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #304111 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=304111\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming that you meant the second equation to be x-12=1/2(y-12), the equations look right to me.  When I solved the system that you have, I got James=24 and Mari=36 years present age.  Of course in 5 years they will be 5 years older so the answer to the question should be J+5=29 and M+5=41.  You mentioned that you were solving this system by graphing, and you said the lines did not intersect!  Maybe you did not extend the graph far enough.  You will need a LARGE graph to contain the point (24,36).  \r<BR>\n" );
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document.write( "Here is the graph of the two lines.  If you are using a graphing calculator, like the one in algebra.com, you will need to solve for y in each of the equations.  Then most importantly, be sure to make the window of the calculator large enough.  I'm using x and y from -10 to 50 .\r<BR>\n" );
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document.write( "a) 9x-4y=72<BR>\n" );
document.write( "   -4y = -9x + 72<BR>\n" );
document.write( "     y=(9x-72)/4\r<BR>\n" );
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document.write( "b) x-12=1/2(y-12)<BR>\n" );
document.write( "   2(x-12)=y-12<BR>\n" );
document.write( "    y=2(x-12) + 12\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C+-10%2C50%2C-10%2C50%2C+%289x-72%29%2F4%2C+2%28x-12%29%2B12%29+ ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C+-10%2C50%2C-10%2C50%2C+%289x-72%29%2F4%2C+2%28x-12%29%2B12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "As you can see, the lines DO actually intersect!!  \r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje, Retired<BR>\n" );
document.write( "Seminole State College of Florida </SPAN>\n" );
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