Find the equation of the line passing through the point of intersection of the lines 4x – 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.

Given:

4x − 7y − 3 = 0 … (1)

2x − 3y + 1 = 0 … (2)

To find:

Equation of line passing through the point of intersection of lines.

Concept Used:

Point of intersection of two lines.

Explanation:

Solving (1) and (2) using cross - multiplication method:

⇒ x = - 8 , y = - 5

Thus, the point of intersection of the given lines is ( - 8, - 5).

Now, the equation of a line having equal intercept as a is

This line passes through ( - 8, - 5)

⇒ - 8 - 5 = a

⇒ a = - 13

Hence, the equation of the required line is or x + y + 13 = 0