Question

the value of K for which the system of equation Kx -2y-3=0 and 3x +y-5=0 has unique solution is

Answer 1

FOR THE EQUATION,
kx-2y-3=0
kx-2y=3

comparing with a1x+b1y=c1

a1=k,b1=-2,c1=3

FOR THE EQUATION
3x+y-5=0
3x+y=5

comparing with a2x+b2y=c2

a2=3,b2=1,c2=5

THESE HAVE UNIQUE SOLUTION

SO,

a1/a2 is unequal to b1/b2
calculations are shown in the image


we get
k is not equal to -6.

Therefore,
the equation will have a unique solution for all values of k except -6.

hope this helps!!!