Finding the probability of an event using set theory Given: $P(A \cup B) = 0.7$, $P(A \cup B') = 0.9$, 
Find $P(A)$.
I feel like the answer has something to do with the property that 
$P(A \cup B) = P(A) + P(B) - P(AB)$ and $P(A \cup B') = P(A) + P(B') - P(AB')$, but I don't know how to get rid of $B$ and $B'$ using the properties. Thanks for any help.

P(A u B) + P(A u B') = P(A) + P(B) - P(AB) + P(A) + P(B') - P(AB')
0.7 + 0.9 = P(A) + P(B) - P(AB) + P(A) + P(B') - P(AB')
1.6 = 2P(A) + P(B) + P(B') - [P(AB) + P(AB')]
1.6 = 2P(A) + P(B) +P(B') - P(A)                                                   [law of total probability]
1.6 = P(A) +P(B) + P(B')
1.6 = P(A) + 1                                                                                  [P(B) + P{B') = 1]
P(A) = 0.6
