Question

For value of k will the following pair of linear equations have no solution? 3x+y=1
(2k-1) x+(k-1)y =2k+1

Answer 1

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Answer 2

Given:

3x+y=1

(2k-1) x+(k-1)y =2k+1 have no solution

To Find:

The value of k

Solution:

Two equations has a unique solution when: a1/a1≠ b1/b2

Two equations has no solution when:  a1/a2= b1/b2 ≠c1/c2

Two equations has an infinite number of solutions when: a1/a2= b1/b2= c1/c2

According to the question,

3x+y=1

(2k-1) x+(k-1)y =2k+1

These equations have no solution

so,

a1/a2= b1/b2 ≠c1/c2

where

a1=3           b1 =1          c1 = -1

a2=(2k-1)    b2=(k-1)     c2=-(2k+1)

a1/a2 = 3/(2k-1)

b1/b2 = 1/(k-1)

On comparing a1/a2 and b1/b2

3/(2k-1) =1/(k-1)

(2k-1)=3(k-1)      (By cross multiplication)

2k-3k = -3+1

k = 2

Hence, the value of k is 2.