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.

Let the equation of the line having equal intercepts on the axes be

=> x + y = 1 ---------------- (1)

On solving equations 4x + 7y – 3 = 0 and 2x – 3y +1 = 0, we get

Thus,

is the point of intersection of the two given lines.

Since, equation (1) passes through point

⇒ a =

Thus, Equation (1) becomes

, i.e., 13x + 13y = 6

Therefore, the required equation of the line 13x + 13y = 6.