Abottle 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.

The first answer is correct