Find the solutions of following question

(i) Comparing equation 2x + 3y – 7 = 0 with a1x +b1y + c1 = 0 and (a − b) x + (a + b)

y − 3a – b + 2 = 0 with a2x +b2y + c2 = 0

We get and and

Linear equations have infinite many solutions if

⇒

⇒ 2a + 2b = 3a − 3b and 6 − 3b − 9a = −7a − 7b

⇒ a = 5b… (1) and −2a = −4b – 6… (2)

Putting (1) in (2), we get

−2 (5b) = −4b – 6

⇒ −10b + 4b = −6

⇒ −6b = –6 ⇒ b = 1

Putting value of b in (1), we get

a = 5b = 5 (1) = 5

Therefore, a = 5 and b = 1

(ii) Comparing (3x + y – 1 = 0) with a1x +b1y + c1 = 0 and (2k − 1)x + (k − 1)y −2k – 1 = 0) with a2x +b2y + c2 = 0,

We get and and c2 = −2k − 1

Linear equations have no solution if

⇒

⇒ 3 (k − 1) = 2k – 1

⇒ 3k – 3 = 2k − 1

⇒ k = 2