$\dfrac{x-a}{m}=\dfrac{y-b}{n}=\dfrac{x-a+y-b}{m+n}=\dfrac{k-a-b}{m+n}$
$→\dfrac{x-a}{m}=\dfrac{k-a-b}{m+n}$
$x-a=\dfrac{(k-a-b).m}{m+n}$
$x-a=\dfrac{ka-am-bm}{m+n}$
$x=\dfrac{ka-am-bm}{m+n}+a$
$x=\dfrac{ka-am-bm}{m+n}+\dfrac{a(m+n)}{m+n}$
$x=\dfrac{ka-am-bm+am+an}{m+n}$
$x=\dfrac{ka-bm+an}{m+n}$
$→\dfrac{y-b}{n}=\dfrac{k-a-b}{m+n}$
$y-b=\dfrac{(k-a-b).n}{m+n}$
$y-b=\dfrac{kn-an-bn}{m+n}$
$y=\dfrac{kn-an-bn}{m+n}+b$
$y=\dfrac{kn-an-bn}{m+n}+\dfrac{b(m+n)}{m+n}$
$y=\dfrac{kn-an-bn+bm+bn}{m+n}$
$y=\dfrac{kn-an+bm}{m+n}$
Vậy $x=\dfrac{ka-bm+an}{m+n}, y=\dfrac{kn-an+bm}{m+n}$
