Answer
$$a=\frac{1}{2},c=849,b=\frac{49}{2}$$
Work Step by Step
We first write the three equations: $$ 927=(3^2)\cdot a+b(3)+c \\ 1179=(11^2)\cdot a+b(11)+c \\ 1495=(19^2)\cdot a+b(19)+c$$ We solve for a in the first equation: $$ 1495=(19^2)\cdot a+b(19)+c$$ We plug in a into the next two equations: $$ 1179=\frac{-264b-112c+112167}{9} \\ 1495=\frac{-912b-352c+334647}{9}$$ Solving for b in the second equation: $$1495=\frac{-912b-352c+334647}{9} $$ Plugging into the third equation: $$1495=\frac{-912(-\frac{7(4c-3627)}{66})-352c+334647}{9} \\ c=849$$ Thus: $$b=-\frac{7(4\cdot 849-3627)}{66} \\ b=\frac{49}{2}$$ And: $$a=\frac{927-3\cdot \frac{49}{2}-849}{9}\\ a=\frac{1}{2}$$
