



 
Hi Harold, You sent us you solution
which is method I would have used also. Then you asked
I sketched a graph of each equation using the intercepts. So for the equation 2x  3y = 6 I used the points (0, 2) and (3, 0) and for the equation x  3y = 2 I used (0, 2/3) and (2, 0). I put marks at the integer points on the axes and you can see that the xcoordinate of the intersection point P on my graph is close to 4 but not exactly 4. The problem arises from trying to place the point (0, 2/3) where the ycoordinate is a fraction. I might have been better for the line x 3y = 2 to use the points (2, 0) and (5, 1). Even then I doubt that the graph would allow me to conclude that the ycoordinate of P is 2/3. I am not at all downplaying the use of the graphical method but I use it most often to give an estimate of the answer or a confirmation of the answer obtained by an algebraic technique. Even in my rough graph above I can see that the xcoordinate of P is approximately 4 and the ycoordinate is between 1/2 and 1. Hence I have some confidence that the solution (4, 2/3) is correct. Penny  


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