I need to find the equation of the cubic curve that passes through four points $(1,-126)$, $(8,840)$, $(-6,280)$ and $(-11,270)$. 

Using the form $y = ax^3 + bx^2 +cx +d$, I produced $4$ equations:

From $(-11,270):-1331a+121b-11c+d=270,$

From $(-6,280):-216a+36b-6c+d=280,$

From $(8,840): 512a+64b+8c+d=840,$

From $(1,-126): a+b+c+d=-126,$

I have attempted to solve these by elimination, subtracting each equation by the one below (excluding the bottom), but the answer doesn't satisfy all points. With slight changes to my method, it has produced several different answers that never intersect all $4$ points. 

Am I just making a mistake in subtraction, or do I need to use a different method? Can a simultaneous equation have no solutions? Any help would be very much appreciated.