The equation which cannot be solved in integers is

(a) Given equation is 5y – 3 = –18

⇒ 5y = – 18 + 3 [transposing 3 to RHS]

⇒ 5y = –15

⇒ [dividing both sides by 5]

⇒ y = –5 (integer)

(b) Given equation is 3x – 9 = 0

⇒ 3x = 9 [Transposing 9 to RHS]

⇒ [Dividing both sides by 3]

⇒ x = 3 (integer)

(c) Given equation is 3z + 8 = 3 + z

On transposing z and 8 to LHS and RHS respectively, we get

⇒ 3z – z = 3 – 8

⇒ 2z = –5

⇒ [dividing both sides by 2]

⇒ (neither a positive fraction nor an integer)

(d) Given equation is 9y + 8 = 4y – 7

On transposing 4y and 8 to LHS and RHS respectively, we get

⇒ 9y – 4y = –7 – 8

⇒ 5y = –15

⇒ [Dividing both sides by 5]

⇒ y = – 3 (integer)