Question

Find the equation of the line passing through the point of intersection of 7x + 6y = 71 and 5x – 8y = −23; and perpendicular to the line 4x – 2y = 1.

Answer 1

7x + 6y = 71 `=>` 28x + 24 = 284  ...(1)

5x − 8y = −23 `=>` 15x − 24y = −69    ...(2)

Adding (1) and (2), we get,

43x = 215

x = 5

From (2),

8y = 5x + 23

= 25 + 23

= 48

`=>` y = 6

Thus, the required line passes through the point (5, 6).

4x − 2y = 1

2y = 4x − 1

`y = 2x - 1/2`

Slope of this line = 2

Slope of the required line =`(-1)/2`

The required equation of the line is

y – y₁ = m(x₁,x₂)

`y - 6 = (-1)/2 (x - 5)`

2y − 12 = −x + 5

x + 2y = 17