A day full of math games & activities. Find one near you.

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is
a. -5/4
b. 2/5
c. 15/4
d. 3/2

Solution:

Given, the linear pair of equations are

3x + 2ky = 2

2x + 5y + 1 = 0

We have to find the value of k.

We know that,

For a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If \(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}\neq \frac{c_{1}}{c_{2}}\), then the graph will be a pair of parallel lines.

Here, a₁ = 3, b₁ = 2k, c₁ = -2

a₂ = 2, b₂ = 5, c₂ = 1

So, a₁/a₂ = 3/2

b₁/b₂ = 2k/5

c₁/c₂ = -2/1 = -2

By using the above result,

\(\frac{3}{2}=\frac{2k}{5}\)

On cross multiplication,

3(5) = 2(2k)

15 = 4k

So, k = 15/4

Therefore, the value of k is 15/4.

✦ Try This: If the lines given by 2x + 3ky = 2 and 3x + 5y + 1 = 0 are parallel, then the value of k is

Given, the linear pair of equations are

2x + 3ky = 2

3x + 5y + 1 = 0

We are required to find the value of k.

Here, a₁ = 2, b₁ = 3k, c₁ = -2

a₂ = 3, b₂ = 5, c₂ = 1

So, a₁/a₂ = 2/3

b₁/b₂ = 3k/5

c₁/c₂ = -2/1 = -2

By using the above result,

\(\frac{2}{3}=\frac{3k}{5}\)

On cross multiplication,

2(5) = 3(3k)

10 = 9k

So, k = 10/9

Therefore, the value of k is 10/9

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.1 Problem 7

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is, a. -5/4, b. ⅖, c. 15/4, d. 3/2

Summary:

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is 15/4

☛ Related Questions: