Question

A line passes through the point of intersection of the lines 3x + y + 1 = 0 and 2x – y + 3 = 0 and makes equal intercepts with axes. The equation of the line is ______.

Options

• 5x + 5y – 3 = 0

• x + 5y – 3 = 0

• 5x – y – 3 = 0

• 5x + 5y + 3 = 0

Answer 1

A line passes through the point of intersection of the lines 3x + y + 1 = 0 and 2x – y + 3 = 0 and makes equal intercepts with axes. The equation of the line is 5x + 5y – 3 = 0.

Explanation:

The point of intersection of the lines 3x + y + 1 = 0 and 2x – y + 3 = 0 are `((-4)/5, 7/5)`.

The equation of line which makes intercepts with the axes is x + y = a.

∴ `- 4/5 + 7/5` = a ⇒ a = `3/5`

∴ The required equation of the line is

`x + y - 3/5` = 0  i.e., 5x + 5y – 3 = 0