To do elimination, you need to make it so that one of the variable terms will cancel itself out. In other words, you need to be able to add two of one term together and get 0.
In this case, it's easiest to do that by making the x term in the second equation be -9x. So we mulitply that equation by 9. So now that equation is
72y - 9x = -630.
So now you can add the two equations together and you get
67y = -603
Divide both sides by 67 and you get y = -9.
Plug that back into the second equation to solve for x. Then you get
-72 - x = -70
-x = 2
x = -2