Question

Let x – 3 = y and ky – x + 6 = 0 represent a pair of parallel lines then K=____​

Answer 1

Step-by-step explanation:

We have,

$x - 3 - y = 0 ............(i) \\ ky - x + 6 = 0.............(ii)$

The given pair of equations are in the form of

$a1x1 + b1y1 + c1 = 0 \\ a2x2 + b2y2 + c2 = 0$

where,

a1=1, a2=k,

b1=-3 , b2=-1

c1=-1 , c2=6

We know that if a pair linear equation in two variables represent parallel lines in the coordinate plane, then they have no solution.

So,For no solution,the condition is,

a1/a2=b1/b2≠c1/c2

So,

1/k=3/1≠-1/6

Here,1/k=3 and 1/k≠-1/6

or,k=3 and k≠-6

Hence,the value of k is 3