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

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- Solution iv

Solution

At

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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