Question

If the lunes given by 3x+2ky=2 and 2x +5y+1=0 are paralllel find the value of k

Answer 1

ANSWER

given equations

3x+2ky = 2 ..........(1)

2x+5y= -1............(2)

CONCEPT

for method 1

• slope of a line is given by

$x = - \frac{a}{b} = \frac{ - coeff \: ofx}{ceff \: of \: y}$

for method 2

• the equations of two perpendicular line differ only in constant term . coefficient of x and y are same for eq of parallel lines.

SOLUTION

method 1

slope of line 1 = slope of line 2

$\frac{ - 3}{ \: 2k} = \frac{ - 2}{5} \\ or \: \: k \: = \: \frac{15}{4}$

method 2(shortcut)

in given equations coefficient of x is different so first make coefficient of x same for both

multiply first by 2

second by 3

we get

6x+4ky -4 = 0

6x+15y+3 = 0

now,

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

hope it helps

Answer 2

Answer:

Given that,

3x+2ky=2 and 2x+5y+1=0

2x+5y=-1

a1=3, b1=2k, c1=2, a2=2, b2=5, c2=-1

To which the equations are parallel.

a1/a2=b1/b2≠c1/c2

3/2=2k/5

3×5=2×2k

15=4k

4k=15

k=15/4

when k=15/4, the given equations represent parallel lines.