Let 'x' be Jim's weekly payment and 'y' Alicia's. Than 'x' and 'y' are non-negative numbers. We need to find x and y.

Jim's weekly pay is two thirds of Alicia's:

x = (2/3) y

Together they earn $600 per week meaning:

x + y =600

If we replace x = (2/3) y in x + y =600 we get:

(2/3) y + y = 600

(2 + 3) y /3 = 600

5y = 600 * 3

y = 1800 / 5

y = 360 dollars is the weekly pay of Alicia.

x = (2/3) y = (2/3) * 360 = 240 dollars is the weekly pay of Jim.