 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/12/b/iv/solution

a = 1

, the reduced system gives

z = 1

and

x + y = 2

. Thus all solutions are

(x, y, z) = (2 - s, s, 1), s \in R .

Geometrically the solution set is an affine straight line, and substitution verifies all three original equations.

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