Question

Find the value of k if the pair of linear equations 2x-3y=8 and 2(k-4)x-ky=k+3

Answer 1

Given:

The pair of linear equations 2x-3y=8 and 2(k-4)x-ky=k+3

To find:

Find the value of k if the pair of linear equations 2x-3y=8 and 2(k-4)x-ky=k+3

Solution:

From given, we have,

The pair of linear equations 2x-3y=8 and 2(k-4)x-ky=k+3

The condition for a pair of linear equations to be consistent intersecting lines is,

a1/a2 = b1/b2 ≠ c1/c2

⇒ 2/2(k-4) = -3/-k ≠ -8/-(k+3)

Now consider,

2/2(k - 4) = -3/-k

2/2(k - 4) = 3/k

2k = 3[2(k - 4)]

2k = 6k - 24

24 = 6k - 2k = 4k

k = 6