Question

The pair of linear equations 2kx + 5y – 7 = 0, 6x – 5y – 1 = 0 has a unique solution if the value of k is

(a)K - 3 (b) k 3 (c) k 5 (d) k - 5​

Answer 1

Answer:

for unique solutions, a1/a2 not equal to b1/b2

2k/6 not equal to 5/-5

2k not equal to 5/-5 × 6

2k not equal to 30/-5

2k not equal to -6

k not equal to -6/3

k not equal to -2.

All the values of k are possible except -2

Answer 2

Answer:

k ≠ - 3

Step-by-step explanation:

Given :

2 k x + 5 y – 7 = 0  ...( i )

6 x – 5 y – 1 = 0   ... ( ii )

Pair of linear equations has a unique solution .

We know for unique solution.

$\large \dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}$

Comparing from ( i ) and ( ii ) we have

$\large a_1=2k \ a_2=6 \ b_1=5 \ and \ b_2=-5$

Put these values in formula.

$\large \dfrac{2k}{6}\neq\dfrac{5}{-5}\\\\\\\large \dfrac{k}{3}\neq\dfrac{1}{-1}\\\\\\\large k\neq -3$

Thus we get answer many values of k but leaving k ≠ -3.