A bottle filled with water weighs 1kg. The same bottle filled 1/3 with water weighs 640g. What is the weight of the bottle? (1kg=1000g)

The bottle alone weighs x grams and the water in the full bottle weighs y grams.

Write two equations.

This problem is easily solved without system of equations.

Bottle + water = 1000 g

bottle + 1/3 water = 640 g

Subtract to get 2/3 water = 360 g

so water weighs 360 / (2/3) = 540 g

bottle weighs 1000-540=460 g

Using equations

B=weight of bottle

W=weight of water

the two equations are

B+W=1000

B+W/3=640

For the purpose of the question, use x=bottle, y=water.

However, it is always a better idea to use letters that tell you something than x, y.