Question

Please help with system of equasions

Answer 1

The slope of line $m$ is $\frac{-3-1}{2-6}=1$, so its equation is

$y-1=x-6\implies y=x-5$

The slope of line $n$ is $\frac{-6-3}{5-2}=-3$, so its equation is

$y-3=-3(x-2)\implies y=-3x+9$

The two lines intersect wherever the two equations are the same:

$x-5=-3x+9\implies4x=14\implies x=\dfrac72\implies y=-\frac32$

The point of intersection is then $\left(\frac72,-\frac32\right)$.