Question

Find the value of k so that the system of equation x-2y=3 and 2x+ky=7 has a unique solution​

Answer 1

The given system of equations is:

  x - 2y = 3

2x + ky = 7

The above equations are of the form

  a1 x + b1 y − c1 = 0 

a2 x + b2 y − c2 = 0  Here,

a1 = 1, b1 = -2, c1 = 3 

a2 = 2, b2 = k, c2 = 7  So according to the question,  For unique solution, the condition is 

a1/a2 ≠ b1/b2

  1/2not = -2/k ⇒ k ≠ -4

  Hence, the given system of equations will have unique solution for all real values of k other than -4.