Question

Find the equation of the line passing through the intersection of the lines 4x+3y=1 and 5x+4y=2

Answer 1

Answer:

Firstly , we should find out intersecting point of given lines 5x -3y = 1 and 2x + 3y = 23.

5x - 3y = 1 ------(1)

2x + 3y = 23 ------(2)

add equations (1) and (2) ,

7x = 24 ⇒ x = 24/7 , put it in equation (1)

3y = 120/7 -1 ⇒y = 113/21

Hence, unknown line is passing through the point (24/7 , 113/21)

now, unknown line is perpendicular upon 5x - 3y = 1

Means, slope of unknown line ×{ slope of 5x - 3y = 1} = -1

Let slope of unknown line is m

∴ m × 5/3 = -1 ⇒ m = -3/5

Now, equation of unknown line is ,

(y - 113/7) = -3/5(x - 24/7)

⇒5y - 565/7 + 3x - 72/7 = 0

⇒ 3x + 5y - 91= 0

Hence, answer is 3x + 5y = 91