Question 440130
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).  


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 .


a) 9x-4y=72
   -4y = -9x + 72
     y=(9x-72)/4


b) x-12=1/2(y-12)
   2(x-12)=y-12
    y=2(x-12) + 12

{{{graph(400,400, -10,50,-10,50, (9x-72)/4, 2(x-12)+12) }}}


As you can see, the lines DO actually intersect!!  


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida