Q. 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. Then, equation of the line is
A) $5x + 5y - 3 = 0$
B) $x + 5y - 3 = 0$
C) $5x - y - 3 = 0$
D) $5x + 5y + 3 = 0$
Explanation
(a)
The point of intersection of the lines $3x + y + 1 = 0$ and $2x - y + 3 = 0\left( - \frac{4}{5},\frac{7}{5} \right)$. The equation of line which makes equal intercepts with axes is $x + y = a$
$\therefore\ - \frac{4}{5} + \frac{7}{5} = a\ \Rightarrow \ a = \frac{3}{5}$
$\therefore$ Equation of line is $x + y - \frac{3}{5} = 0$
$or\ 5x + 5y - 3 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.