let

l = the mass of one large pebble

s = the mass of one small pebble

b = the mass of the basket

The total mass of a basket, 4 large pebbles, and 2 small pebbles is 7/12 kilogram

b + 4l + 2s = 7/12

The total mass of the basket, 2 large pebbles and 1 small pebble is 5/12 kilogram

b + 2l + s = 5/12

Multiply both sides of the equation b + 2l + s = 5/12 by 2 and subtract the equation b + 4l + 2s = 7/12

2(b + 2l + s) - (b + 4l + 2s) = 2*(5/12) - 7/12

2b + 4l + 2s - b - 4l - 2s = 5/6 - 7/12

b = 5/6 - 7/12

by solving we find

b = 0.25 kg

click here to see the step by step solution

Click to see all the steps

the mass of the empty basket is 0.25 kg.