Two jugs are filled with water. if you remove 1 liter of water from the first jug, then the two jugs contain the same amount of water. if you remove 2 liters from the second, then the second jug would contain half as much as the first. how many liters of water are in the largest jug?

Let x be the first jug, y the second jug.

From first statement, subtracting 1 from x, makes them equal:
x - 1 = y

From second statement, subtracting 2 from y, makes it half of x:
x/2 = y-2

Solve system with substitution:
x/2 = (x-1) -2
x/2 = x - 3
x- x/2 = 3
x/2 = 3
x = 6

y = x-1 = 6-1 = 5

Therefore the largest jug contains 6 liters.