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If: y = x-4 and x^2+y^2 = 8 then x^2+(x-4)^2 = 8

Multiply out the brackets and subtract 8 from both sides:-

So: x^2+x^2-8x+16-8 = 0 => 2x^2-8x+8 = 0

Solving the above quadratic equation: x = 2 or x = 2 which are both equal roots

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