23base(x) +12base(y) =21base(10)

Answer 1

x + y = 10

Answer 2

2x+3 + y+2 = 21
2x+y = 16
so the solutions are
x=4,y=8: 23₄ + 12₈ = 11+10 = 21
x=5,y=6: 23₅ + 12₆ = 13+8 = 21
x=6,y=4: 23₆ + 12₄ = 15+6 = 21