The numbers 1 through 8 are to be placed in the circles in the diagram shown such that the sum of the numbers on each side of the figure is 15. Find the values of x, y, and z. Then copy the diagram on a piece of paper and fill in each circle with the appropriate number. Be sure to show all your work. Upload the finished problem below.
Note: x satisfies –4(x – 2) = –4,
y satisfies 9 + 2(y – 3) = 3(y – 2) + 1,
and z satisfies z/3 + 1/2 = 5/2.