Question

find the value of k for which the following pair of linear equation has a unique solution 2x+3y=7;(k-1)x+(k+2)y=3k

Answer 1

The given pair of linear equations can be rewritten as:

1) 2x+3y-7=0                         and;           2) (k-1)x+(k+2)y-3k=0

Here,

a1=2     b1=3     c1=-7

a2=(k-1)    b2=(k+2)   c2=-3k

So, for a unique solution (intersecting lines):-

a1/a2≠b1/b2

⇒2/(k-1) ≠ 3/(k-2)

⇒2k-2 ≠ 3k-3

⇒2k-3k ≠ -3+2

⇒ k ≠ 1

Hence, for every value of k other than 1 , the given pair of linear equations will have a unique solution.

Hope this helps.

Answer 2

Answer

Hope it will help