Question

Find equation of a line which passes through point $(2,-3)$ and the point of intersection of the lines $x+y+4=0$ and $3x-y-8=0$

Answer 1

Given the equation of the lines,

$x+y=-4$.....(1) and $3x-y=8$.....(2).

Solving (1) and (2) we get, $x=1,y=-5$.

Now the equation of the line passing through the points $(2,-3)$ and $(1,-5)$ is,

$\frac{y+3}{-5+3}=\frac{x-2}{1-2}$

or, $y+3=2(x-2)$

or, $y-2x=-7$.