Find the values of a and b for which the following system of equations has infinitely many solutions:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
For infinitely many solution
⇒ 6a – 3 = 15 and -9 = 5b – 10
⇒ a = 3 and b = 1/5
(ii) For infinitely many solution
⇒ 6 = 2b + 1 and 6a + 15 = 9
⇒ b = 5/2 and a = -1
(iii) For infinitely many solution
⇒ 3a – 3 = 6 and 9 = 1 – 2b
⇒ a = 3 and b = -4
(iv) For infinitely many solution
⇒ 15a – 3 = 12a + 12b and 20a – 4 = 24a – 24b
⇒ 3a – 12b = 3 ------ (1) and 6b – a = 1 ------ (2)
Multiplying eq2 by 3 and adding to eq1
⇒ 6b = 6
⇒ b = 1
Thus, 3a – 12 = 3
⇒ a = 5
(v) For infinitely many solution
⇒ 2a + 2b = 3a – 3b and 6a + 2b – 4 = 7a – 7b
⇒ a = 5b and 9b – a = 4
Thus, 9b – 5b = 4
⇒ b = 1
⇒ a = 5
(vi) For infinitely many solution
⇒ 2a + 2 = 3a – 3
⇒ a = 5
(vii) For infinitely many solution
⇒ 2a + 4 = 3a – 3
⇒ a = 7