geometry

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how to solve
y= (x-2)^2+4
4x+2y=14
algebraically

  • geometry -

    By substitution:
    y= (x-2)^2+4 ....(1)
    4x+2y=14 ....(2)
    Solve for y from (2) divided by 2:
    2x+y=7
    y=7-2x ...(2a)

    Substitute (2a) in (1)
    7-2x = (x-2)^2+4
    Expand
    7-2x = x^2-4x+4+4
    x^2 -2x +1 = 0 ....(1a)

    Solve 1(a) to get:
    x=1 (duplicity 2)

    Now substitute x=1 in (2a) to get
    y=5

    Substitute x=1,y=5 in (1) to check:
    (1-2)^2+4 = 5 OK.

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