The point $(1,5)$ satisfies the simultaneous equations $n^2x+my=14$ and $ny-mx=8$ . Find one valid pair of values for $n$ and $m$ .

Model answer

n=2, m=2

Also accepted: n=2,m=2, 2 and 2

Explanation: Substituting

(1,5)

gives

n^2+5m=14

and

5n-m=8

, leading to

n^2+25n-54=0

, i.e.

(n+27)(n-2)=0

. This gives two valid solution pairs:

(n,m)=(2,2)

(n,m)=(-27,-143)

; the simpler pair

(2,2)

is accepted here.

Derived from ZIMSEC Pure Mathematics Paper 2, November 2025, Q6

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