Question

Find the distance between the following parallel lines. 5x-3y-4=0,10x-6y-9=0​

Answer 1

Answer:

To Find the distance between these parallel lines , we need to find the value of x and y .

Step-by-step explanation:

5x - 3y- 4 = 0

5x - 3 y = 0 + 4

5x - 3 y = 4 --------------- eqn 1.

10x - 6 y - 9 = 0

10x - 6y = 0 + 9

10× - 6y = 9 ------------------eq n 2.

Now , multiply eqn 1. by 2n

2 ( 5x - 3y = 4)

10× - 6y = 8 -------------------eqn 3.

Now , lets add eq n 3. from 2.

10 x - 6y = 9

10 x - 6y = 8

---------------------

20 x - 12 y = 17

20 x = 17 + 12 y

x = 17 + 12 y / 20

Now ,lets put the value of x in eqn 2.

10x - 6y = 9

10 × 17 + 12y / 20 - 6y = 9

17 - 12 y / 2 - 6y = 9

17 - 12 y - 12 y / 2 = 9

17 - 24 y = 9 × 2

17 - 24 y = 18

- 24 y = 18 - 17

y = 1 / -2 4

Put y = 1 / - 24 in eq 1.

5x - 3 y = 4

5x - 3 × 1 / -24 = 4

5x - 1 / -8 = 4

5x - 1 = 4 × (-8)

5x - 1 = -32

5x = -32 + 1

5x = -31

x = -31 / 5

:- ( x , y )

:- ( -31/ 5 , 1 / - 24)

Hope it will help you ......