Question

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

• A. \(-7\)
• B. \(\frac {10}{3}\)
• C. \(-13\)
• D. \(-\frac {10}{3}\)

Answer 1

The Correct Option is D

To solve the problem, we need to find the value of $k$ such that the lines $2x + ky = 1$ and $3x - 5y = 7$ are parallel.

1. Understanding the Condition for Parallel Lines:

Two lines are parallel if their slopes are equal.

The general form of a line is $Ax + By = C$. The slope of such a line is given by:

$ m = -\frac{A}{B} $

2. Finding the Slope of the Second Line:

For the line $3x - 5y = 7$:

$ A = 3 $, $ B = -5 $

Slope $ m = -\frac{3}{-5} = \frac{3}{5} $

3. Finding the Slope of the First Line:

For the line $2x + ky = 1$:

$ A = 2 $, $ B = k $

Slope $ m = -\frac{2}{k} $

4. Setting Slopes Equal:

Since the lines are parallel:

$ -\frac{2}{k} = \frac{3}{5} $

5. Solving for $k$:

Multiply both sides by $k$ and then solve:

$ -2 = \frac{3k}{5} $

Multiply both sides by 5:

$ -10 = 3k $

$ k = \frac{-10}{3} $

Final Answer:

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