ANSWER:

If a pair of LINEAR  equations is given by

a1x  +  b1y  +  c1 = 0

a2x  +  b2y  +  c2 = 0

When the system of linear equations will represent two Parallel Lines there is no point of intersection and consequently there is no pair of values of x and y which satisfy both equation. Thus, system has no solution and such pair of linear equation is inconsistent pair of  linear equations

For parallel lines (inconsistent) :

a1 /a2 = B1/b2 ≠ c1/ c2

SOLUTION:

The Given pair of  linear equation is :

kx  + 3y  =  k - 3 …………(1)

12x  +  KY  =  k……………..(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=k , b1= 3, c= - (k-3)

a2= 12 , b2= k , c= -k

a1/a2= k /12 ,  b1/b2=  3/k , c1/c2 = -(k-3)/-k

Given: A pair of linear equations will be inconsistent (Parallel) and has no Solution,if

a1 /a2 = b1/b2 ≠ c1/ c2

k/12 = 3/k ≠ -(k-3)/-k……..(3)

(I)        (II)        (III)

On  taking I & II terms

k/12 = 3/k

k × k = 12 × 3

k² = 36

k =√36

k = ±6

Since k = 6 does not satisfy the last two terms of equation 3.

Therefore , k = -6 is the required value.

Hence, for k = - 6 the given system of equations will be inconsistent.

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Step-by-step explanation: