Question

Find the value of k so that the pair of linear equations x- 2y=3 and 3x+y=5 has a unique solution

Answer 1

given:

find : k

Solution:
The Given pair of  linear equation is :

3x +2y = -5
3x +2y +5= 0………(1)

x -ky=2
x -ky -2 = 0…………(2)

On comparing with General form of a pair of linear equations  in two variables x & y is: a1x + b1y + c1 = 0
and   a2x+b2y + c2= 0

a1= 3, b1= 2, c= 5
a2= 1 , b2= -k , c= -2

a1/a2= 3/1 ,  b1/b2= 2/-k &
A pair of linear equations has a Unique solution if

a1/a2 ≠ b1/b2 
3/1 ≠ 2/-k
3× -k ≠ 2
k ≠ -⅔

Hence, the value of k ≠ -⅔.