Question

If the lines given by 2x+ky=1 and 3x-5y=7 are parallel, then the value of k is

Answer 1

Given,

Two parallel lines 2x+ky=1 and 3x-5y=7

To Find,

value of k

Solution,

Two lines are said to be parallel if they have equal slopes

So, equating the slopes of the given lines

-k/2 = 5/3

k = -10/3

Hence, the value of k is -10/3

Answer 2

Answer:

The value of k = $-\frac{10}{3}$

Step-by-step explanation:

The given lines are 2x +ky = 1 and 3x -5y =7

The line ax + by + c = 0 then slope is -a/b

Given the lines are parallel.

2x +ky = 1  --------------(1)

a = 2, b = k, c = -1

Slope of equation(1) is = $-\frac{a}{b} = -\frac{2}{k}$

3x -5y =7  ----------------(2)

a=3, b= -5, c = -7

Slope of equation(2) = $-\frac{a}{b} = -\frac{3}{-5} =\frac{3}{5}$

The slopes of parallel lines are equal

∴$-\frac{2}{k} =\frac{3}{5}$

⇒ -10 = 3k

⇒ k = $-\frac{10}{3}$

Therefore, the value of k = $-\frac{10}{3}$