 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/3/solution

y = 1 - x

. Substitution into the second gives

x - x^{2} + 2 (1 - x)^{2} = 2, x^{2} - 3 x = x (x - 3) = 0.

Thus

x = 0

x = 3

. The corresponding values of

y

give exactly

(x, y) = (0, 1) or (3, - 2) .

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