How Do We Solve Linear Quadratic Systems?

y = x^2 - 2x  + 2
y - 2x  =  - 2                                 Step 1:  First you have to change this into standard form : Y = MX +B )
  +2x          +2x
 ----------------
 Y = 2x - 2
      

2x - 2 = x^2 - 2x +2                                         Step 2)  Substitute this variable into the quadratic equation
-2x +2           -2x+2
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      0 = X^2 -4x +4                                                       Step 3)  Solve the quadratic equation

0=(x -   2)(x -   2)

   You have to make the equation equal Zero so if it`s positive to make it zero you have to make it negative, so if it`s negative you have to make it Positive.
For example :
                      0 = (x - 2)
                         X has to be positive 2

But if it was 0 = (x +2)
                        X would have to be negative 2

So the value of X is 2 so what you do next is      Step 4) Substitute x value into linear equation to get y value
                  y =  2x- 2 = 2(2)- 2 =  2
                     Solution =  (2,2)