Determine the value of k for which the system of linear equa

Determine the value of k for which the system of linear equations has no solution.

3x y = 5

9x + ky = 4

Solution

The system of equations is 3x - y = 5...(1) and 9x + ky = 4... (2). On multiplying both the sides of the 1st equation by 3, we get 9x - 3y =15....(3). Now, subtraction the 3rd equation from the 2nd equation, we get 9x + ky- 9x +3y = 4 - 15

or, (k + 3)y = - 11. Now, if k + 3 = 0, i.e. if k = -3, the given systemof equations will not have any solution.

On substituting, k = -3 in the 2nd equation, we get 9x -3y = 4 The 3rd equation is 9x -3y = 15 . The LHS of these two equations being equal, we have 4 = 15, which is incorrect. Thus k = -3 will lead to no solution for the given system of equations.