Question

find the value of k for which the pair of equations 3x+ky+2y+5=0,6x-8y+7=0 represent parallel line​

Answer 1

Step-by-step explanation:

here's your answer mate

Answer 2

The value of "k" is -6 for which the pair of equations 3x + ky + 2y + 5 = 0, 6x - 8y + 7 = 0 represent parallel line​

Solution:

Given that,

The pair of equations 3x + ky + 2y + 5 = 0, 6x - 8y + 7 = 0 represent parallel line​

If two lines are parallel, then their slopes are equal

The slope intercept form is given as:

y = mx + c

Where, "m" is the slope of line

Rearrange, 3x + ky + 2y + 5 = 0

3x + y(k + 2) + 5 = 0

y(k + 2) = -3x - 5

$y = \frac{-3x}{k + 2} + \frac{-5}{k + 2}$

On comparing with slope intercept form,

$m = \frac{-3}{k+2}$

Rearrange, 6x - 8y + 7 = 0

8y = 6x + 7

$y = \frac{6x}{8} + \frac{7}{8}$

On comparing with slope intercept form,

$m = \frac{6}{8}$

Since slopes are equal,

$\frac{-3}{k + 2} = \frac{6}{8}\\\\-24 = 6k + 12\\\\6k = -24 - 12\\\\6k = -36\\\\k = -6$

Thus value of "k" is -6

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