Let the system of linear equations x + y + k z = 2 2 x + 3 y - z = 1 3 x + 4 y + 2 z = k have infinitely many solutions. Then the system k + 1 x + 2 k - 1 y = 7 2 k + 1 x + k + 5 y = 10 has :

Step-by-step solution

Linear equations x + y + k z = 2 , 2 x + 3 y - z = 1 and 3 x + 4 y + 2 z = k have infinitely many solutions. Therefore, 1 1 k 2 3 - 1 3 4 2 = 0 ⇒ 1 10 - 1 7 + k - 1 = 0 ⇒ 10 - 7 - k = 0 ⇒ 3 - k = 0 ⇒ k = 3 For k = 3 , the second system of equations is 4 x + 5 y = 7                 … 1 7 x + 8 y = 10             … 2 Clearly, they have a unique solution Subtracting 1   &   2 , we get 3 x + 3 y = 3 &