Let the bigger number be x and the smaller number be y. We have:
x - y = 3 --- (1)
x + y = 13 --- (2)
From (1), we have:
y = x - 3 --- (3)
Substituting (3) into (2), we have:
x + (x - 3) = 13
x + x - 3 = 13
2x = 13 + 3
2x = 16
x = 16 / 2
x = 8
Substituting x = 8 into (3), we have:
y = 8 - 3
y = 5
Hence, x = 8 and y = 5.