Question

For what value of k does the system of equations have no solution : kx+3y=3 and 12x + ky=6

Answer 1

we have,
kx + 3y = 3
=> kx + 3y - 3 = 0 --- (1)
12x + ky = 6
=> 12x + ky - 6 = 0 --- (2)

for the equations (1) and (2) to have no solution,

a1/a2 equal to b1/b2 not equal to c1/c2

Taking b1/b2 not equal to c1/c2,

=> 3/k not equal to -3/-6
=> 3/k not equal to 1/2
=> k×1 not equal to 3×2 [cross multiplication]
=> k not equal to 6
therefore k must be equal to any value other than 6 for the equations to have no solution