Paper 1, Section I, B

Algebra and Geometry | Part IA, 2007

For the equations

px+y+z=1x+2y+4z=tx+4y+10z=t2\begin{gathered} p x+y+z=1 \\ x+2 y+4 z=t \\ x+4 y+10 z=t^{2} \end{gathered}

find the values of pp and tt for which

(i) there is a unique solution;

(ii) there are infinitely many solutions;

(iii) there is no solution.

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