The question

Find the best fit to the set of points {(0, 1) (1, 1) (2, 2) (4, 3)} in within the curve

My attempt

I used the formula , and got the following equation:

I tried to use Gaussian elimination, and made a massive mess of the matrix. I was far off a correct solution. Is there a trick to getting an answer without grinding through row operations (or, at least, minimising the work)?

Cheers.