By multiplying the first equation by (a + c), we obtain

2a + 3b = 2a + 2c
3b = 2c
b = c

Multiplying the second equation by (a + b) gives:

6a + c = 3a + 3b
3a = 3b - c
3a = 3()c - c
3a = c

Now, since b=c and c=3a, b=2a, so the ratio a:b:c can be rewritten as the ratio a:2a:3a, or 1:2:3.