Does more contraception lead to lower abortion rates?

One study looking at abortion in Russia, Belarus and Ukraine:

After adjustment for covariates, the Russian sample experiences higher odds of modern contraception (although the Russian method mix is slightly less efficient). This finding is unexpected given the higher level of abortion in Russia.

Russia: high rates of contraception use. High rates of abortion.

But they're many fewer abortions than there were 20 years ago, you might protest.

Contraception is supposed to SOLVE the problem of unwanted pregnancy. It doesn't. It doesn't even come close.