I read this as 4/(3j)+5/(6k)=13, -1/j+5/k=-3.
Let a=1/j and b=1/k then:
(4/3)a+(5/6)b=13, -a+5b=-3, so a=5b+3.
Substitute for a in the other equation:
(4/3)(5b+3)+(5/6)b=13, that is:
8(5b+3)+5b=78,
40b+24+5b=78,
45b=54, b=54/45=6/5, so k=⅚.
a=5b+3=6+3=9, so j=1/9.
CHECK:
(4/3)9+(5/6)(6/5)=12+1=13 OK;
-9+6=-3 OK.
So solution is (j,k)=(1/9,⅚).