Least squares, what are the new points?

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Let's say I have the following equation system: equation system

The points are graphed as follows: graph of points

Using the least squares method a solution is x =3 and y=1.

According to the solution manual the purpose of the method is to minimise the distance between between the left side and the right hand side of the equation system. This results in: Squared difference

When I substitute the values x=3 and y=1 into the equation system the graph I get is: new graph I thought the new points should be on a line.

My question is:

What is the equation of the line the least squares method results in, or the new points corresponding to each old point?