Let D be the number of dogs up for adoption and C be the number of cats up for adoption. We can set up the following equation to represent the problem:
D + C = 73
C = 2D + 10
Substituting the second equation into the first equation, we get:
D + 2D + 10 = 73
3D + 10 = 73
3D = 63
D = 21
Substituting this back into the second equation, we find that C = 2 * 21 + 10 = 52.
Therefore, there are 21 dogs and 52 cats up for adoption.