Determine whether two languages are context free
For the first one, $$L_1 = \{a^i,b^{i+j}c^j \mid i,j \geq 0 \} $$

Here's an rough idea of the algorithm:


read off the all '$a$'s and push $a$ into the stack
upon seeing a '$b$', pop the '$a$'s till the stack is empty
then again as long as reading '$b$'s keep pushing $b$ into the stack
on seeing a $c$, start popping the stack until empty.




For the second one, 

Please see my answer here, The other answer is equally good (perhaps even better and simpler) than mine.