Question 1166569
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Express  y = {{{(22-4x)/2}}} = 11 - 2x  from the linear equation and then substitute it into the quadratic form.


By doing this way, you will get the quadratic form in one unknown


    x^2 + y^2 = x^2 + (11-2x)^2 = x^2 + 121 - 44x + 4x^2 = 5x^2 - 44x + 121.


Then you can use EITHER Calculus OR the formula for the vertex

      x = " -{{{b/(2a)}}} " = {{{44/(2*5)}}} = {{{22/5}}} = 4.4.
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Solved.