Question

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

Answer 1

Answer:

k = 3.75.

Step-by-step explanation:

Convert each equation to slope-intercept form.

2x + 5y = 1

5y = -2x + 1

y = -0.4x + 0.2.

3x + 2ky = 2

2ky = -3x + 2

y = (-1/5/k) x + 2/2k

y = (--1.5/k)x + 1/k.

If they are parallel then -1.5 / k =-0.4

k = -1.5 / -0.4

So k = 3.75

Answer 2

Answer:

k =  $\frac{15}{4}$

Step-by-step explanation:

Parallel lines have equal slopes.

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange both equations into this form and equate slopes

2x + 5y = 1 ( subtract 2x from both sides )

5y = - 2x + 1 ( divide all terms by 5 )

y = - $\frac{2}{5}$ x + $\frac{1}{5}$ ← in slope- intercept form

with slope m = - $\frac{2}{5}$

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3x + 2ky = 2 ( subtract 3x from both sides )

2ky = - 3x + 2 ( divide all terms by 2k )

y = - $\frac{3}{2k}$ x + $\frac{2}{2k}$ ← in slope- intercept form

with slope m = - $\frac{3}{2k}$

Thus

- $\frac{2}{5}$ = - $\frac{3}{2k}$ ( multiply both sides by - 1 )

$\frac{2}{5}$ = $\frac{3}{2k}$ ( cross- multiply )

4k = 15 ( divide both sides by 4 )

k = $\frac{15}{4}$