The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is no value. Explanation: The given equations of lines are cx – y = 2 and 6x – 2y = 3 ⇒ cx – y – 2 = 0 and 6x – 2y – 3 = 0 Here, a1 = c b1= –1 c1 = –2 And a2 = 6 b2 = –2 c2 = –3 Since, condition for infinitely many solutions is `a_1/a_2 = b_1/b_2 = c_1/c_2` ⇒ `c/6 = (-1)/(-2) = (-2)/(-3)` ⇒ `c/6 = 1/2` and `c/6 = 2/3` ⇒ c = 3 and c = 4 Since, c has different values. So, there exists no value of c for which given equations have infinitely many solutions. |