Question

in pair of linear equation 3x + 2ky= 2 and 2x + 5y+1=0 represent in parallel line then find value of k

Answer 1

Hi !

3x + 2ky -2 = 0
2x + 5y + 1 = 0

a₁ = 3              a₂ = 2    
b₁ = 2k            b₂ = 5
c₁ = -2             c₂ = 1

As the graph of the equation are parallel lines , the equations have no solution
i.e.,

a₁/a₂ = b₁/b₂ ≠ c₁/c₂

3/2 = 2k/5 ≠ -2/1


3/2 = 2k/5

4k = 15
k = 15/4

2k/5 ≠ -2/1

2k/5 ≠ -2

2k ≠ -10

k ≠ -5

The solutions will have nos solution , when the value of k is equal to 15/4 and not equal to -5

k = 15/4
k ≠ -5

Answer 2

Equations are 3x+2ky-2=0 and 2x+5y+1=0
For lines to show parallel lines on graph they must satisfy
a1/a2 =b1/b2 not equal to c1/c2
Here
a1=3, b1=2k and c1=-2
a2=2,b2=5 and c2=1
So
3/2=2k/5not equal to -2/1
3/2=2k/5
15=4k
K=15/4