Find the value of k for which the following pair of linear equations has infinitely many solutions. We have, `2x + 3y = 7 ⇒ 2x + 3y - 7 = 0` For infinitely many solutions `a_1/a_2 = b_1/b_2 = c_1/c_2` ⇒ `(2)/(k+1) = (3)/((2k -1)) = (-7)/-(4k +1)` ⇒ `(2)/(k+1) = (3)/(2k -1)` ⇒ `2(2k + 1) = 3 (k+1)` ⇒`4k - 2 = 3k + 3` ⇒`4k - 3k = 3 +2` `k = 5` or ⇒ `(2)/(k+1) = (-7)/-(4k +1)` ⇒ `2(4k + 1) = 7 (k+1)` ⇒ `8k + 2 = 7k + 2` ⇒`8k - 7k = 7- 2` `k = 5` Hence, the value of k is 5 for which given equations have infinitely many solutions. Concept: Pair of Linear Equations in Two Variables Is there an error in this question or solution? |