Of all the system of equations in x, y and z, ax + by + z = c, x + y = d, y + ez = 1 formed by choosing a, b, c, d, e from the set 0, 1, 2, 3, 4, 5, 6, 7, 8 with replacement, the probability it does not possess a unique solution is 2 m 3 n

Question

Of all the system of equations in x, y and z, ax + by + z = c, x + y = d, y + ez = 1 formed by choosing a, b, c, d, e from the set 0, 1, 2, 3, 4, 5, 6, 7, 8 with replacement, the probability it does not possess a unique solution is 2 m 3 n (in lowest terms), m, n ∈ N. The value of (n – m) is:

Quantrex Academy · Accepted Answer

Correct answer: 3

A = a b 1 1 1 0 0 1 e = a e - b e + 1 (a – b)e + 1 = 0 ∴ (b – a)e = 1 (b – a)e = 1 is possible if e = 1 and (b, a) pair has 8 values ∴ P A = 0 = 8 × 9 × 9 9 5 = 8 9 3 = 2 3 3 6 6 – 3 = 3

Of all the system of equations in x, y and z, ax + by + z = c, x + y = d, y + ez = 1 formed by choosing a, b, c, d, e from the set 0, 1, 2, 3, 4, 5, 6, 7, 8 with replacement, the probability it does not possess a unique solution is 2 m 3 n (in lowest terms), m, n ∈ N. The value of (n – m) is:

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