Simple closed economy problem
Given your equations, you can find

$$Y = C + 50 + 20 \implies Y = C + 70$$

You can then substitute $Y$ for its equal into your other equation

$$C = 100 + 0.5(C + 70 - T)$$

Finally, given a balanced buget, you know that $G = T$, which should be enough for you to solve for $C$.