I like to do these problems without using Chinese Remainder Theorem. Watch how.

Look at 2nd and 3rd equations. Add modulos 17 to first congruence seven times. And add modulos 16 to second congruence seven times. We get,

Since we can combine and get,

Thus, we are left with simply,

(1)

(2)

Look at (1) subtract the modulos 272 once and with (2) subtract modulos 15 ten times, to get,

Since we can combine to get,