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in Mathematics by (73.1k points)

Let S = {(a, b) : a, b ∈ Z, 0 ≤ a, b ≤ 18}. The number of elements (x, y) in S such that 3x + 4y + 5 is divisible by 19 is 

(A)  38

(B)  19

(C)  18

(D)   1 

1 Answer

+1 vote
by (69.1k points)
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Best answer

Correct option (B) 19 

Explanation:

3x + 4y + 5 = 19 I

5 ≤ (3x + 4y + 5) ≤ 131

5 ≤ 19 I ≤ 131

Case (i)
 
Case (ii)
Case (iii)
Case (iv)  Case (v)
Case (vi)

Total Solution = 19

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