mathematical optimization - Fitting a variable using multiple equations

I would like to find the best fit of two variables for a number of approximate equations, such as:

1x+2y+2=7.04
2x+y+4=7.98

1.5x+1.5y-2=2.53
1.8x+3y-1=6.77

That should come up with a result: x = ~1, y = ~2 (exact value for whatever the best fit is).

I can't find any inspiration in either

I don't expect anyone to do it for me, but perhaps someone could push me in a correct direction?

Thanks in advance, r.

Answer

I think this is what you are after:

NMinimize[
 #.# &[Subtract @@@ {
    1 x + 2 y + 2 == 7.04,
    2 x + y + 4 == 7.98,
    1.5 x + 1.5 y - 2 == 2.53,
    1.8 x + 3 y - 1 == 6.77
    }],
 {x, y}]

{0.00360363, {x -> 0.99076, y -> 2.00755}}

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