Let's denote r as raspberries and b as blackberries. We know that there are 7 more raspberries than blackberries, so we can write:
r = 7 + b
Or:
r - b = 7
There are 13 berries in all, which means:
r + b = 13
Now, this is just a system of linear equations:
r - b = 7
r + b = 13
Subtract the two equations:
-2b = -6
Divide by -2:
b = 3
There are 3 blackberries.