Question

For which values of k does the following pair of linear equations have no solution? 2x+3y=1 and (2k-1) x+(k-1) y=2k+1​

Answer 1

Step-by-step explanation:

2x+3y=1...(1)

and (3k−1)x+(1−2k)y=2k+3 ..(2)

The pairs of linear equations have no solution, if

a 1/a 2 = b 1/b 2not equal to c 1/c 2

⇒ 2/3k−1= 3/1−2k

⇒2(1−2k)=3(3k−1)

⇒2−4k=9k−3

⇒13k=5

⇒k= 5/13

Answer 2

Answer:

k = -2

Step-by-step explanation:

2x + 3y = 1

2x+ 3y -1 = 0 (1)

comparing equation 1 with a1x +b1y+c1=0

a1=2

b1=3

c1= -1

now,

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

(2k-1)x +(k-1)y - 2k+1 = 0 (2)

Now, comparing equation 2 with a2x + b2y + c2 = 0

therfore, a2x = (2k-1)

b2=( k-1)

c2 = -(2k+1)

since, linear pair which have no solution is

a1/a2 = b1/b2 not equal to c1/c2

so,

2/2k-1 = 3/ k-1 not equal to 1/(2k+1)

by it , 2/2k-1 = 3/k-1 we get

2k-2 = 3k-3

2k-3k = -3 + 2

so,

k = 1

i/k-1 not equal to 1 = ( 2k+1)

k-1 not equal to 2k+1

k= 2

therefore, for this value the given linear equation has no solution when k= -2