Question

Find the value of k for which each of the following systems of equations have infinitely many solution:
kx-2y+6=04x-3y+9=0

Answer 1

k = 8/3 is the value of k for which each of the following systems of equations have infinitely many solution:  kx-2y+6=04x-3y+9=0

Given,

kx-2y+6 = 0 4x-3y+9 = 0

The condition for equations to have infinitely many solutions is:

Let the equations be, a1x + b1y + c1 = 0 and  a2x + b2y + c2 = 0

a1 / a2 = b1 / b2 = c1 / c2

k/4 = -2/-3 = 6/9

k/4 = 2/3 = 2/3

k/4 = 2/3

3 × k = 2 × 4

3k = 8

k = 8/3