Question

5x+2y=0
x-3y=0

Answer 1

Trivial solution (0,0)

Answer 2

if you put them into y=mx+b you will see that both have y intercept at 0 so (0,0)

Answer 3

|5 2|
A= |1 -3|

since detA != 0, then there are solutions

2y = -5x (*)
3y = x (**)

2y+5*3y = -5x + 5*x
17y = 0
y = 0
x = 3y = 3*0 = 0, from (**)

Ans. x = 0, y = 0