An equation of a straight line passing through the inter-section of the straight lines 3x – 4y + 1 = 0 and 5x + y – 1 = 0 and making non-zero, equal intercepts on the axes is

Equation of any line through the point of intersection of the given lines is (3x−4y+1)+k(5x+y−1)=0or (3+5k)x+(k−4)y+1−k=0or x(k−1)/(3+5k)+y(k−1)/(k−4)=1Since x-intercept = y-intercept⇒k−13+5k=k−1k−4 ⇒ (k−1)(3+5k−k+4)=0⇒ k=1 or k=−7/4For k = 1, (1) becomes 8x – 3y = 0 which makes zero intercepts on the axes.∴ k=−7/4 ⇒ The required equation is4(3x−4y+1)−7(5x+y−1)=0⇒23x+23y=11.