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math

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Solve the system

x^2+y^2-4x+2y=20
4x +3y =5

  • math - Line+circle - ,

    Rewrite
    x^2+y^2-4x+2y=20
    as
    (x-2)^2+(y+1)^2=25=5^2 ...(1)
    represents a circle of radius 5 with centre (2,-1).
    which intersects with the line
    4x+3y=5 ...(2)
    So write
    y=(5-4x)/3 and substitute in the circle equation (1)
    to get (x-2)^2+(((5-4x)/3)+1)^2=5^2
    Solve for x in the above quadratic to get:
    x=5 or x=-1
    Find y accordingly.

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