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

Solution:

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

x/a + y/b = 1

⇒ x + y = ab ....(1)

On solving equations 4x + 7y - 3 = 0 and 2x - 3y + 1 = 0 , we obtain x = 1/13 and y = 5/13

Therefore,

(1/13, 5/13) is the point of the intersection of the two given lines.

Since equation (1) passes through point (1/13, 5/13)

1/13 + 5/13 = a

⇒ a = 6/13

Equation (1) becomes

⇒ x + y = 6/13

⇒ 13x + 13y = 6

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

NCERT Solutions Class 11 Maths Chapter 10 Exercise ME Question 12

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

Summary:

The equation of the line passing through the point of intersection of the line 4x + 7y - 3 = 0 and 2x - 3y + 1 = 0 that has equal intercepts on the axes is 13x + 13y = 6