Question

Find the equation of the straight line passing through origin and the point of intersection of the lines x + 2y = 7 and x – y = 4.

Answer 1

The given equations are:

x + 2y = 7  ...(1)

x − y = 4   ...(2)

Subtracting (2) from (1), we get,

3y = 3

y = 1

From (2),

x = 4 + y

= 4 + 1

= 5

The required line passes through (0, 0) and (5, 1).

Slope of the line = `(1 - 0)/(5 - 0) = 1/5`

Required equation of the line is given by:

y – y₁ = m(x – x₁)

`=> y - 0 = 1/5(x - 0)`

`=>` 5y = x

`=>` x – 5y = 0