the given expression is,
x + 3y = 5
2x - 3y = 1
here the coefficient of y in both the equation is +3y and -3y
it is clear that by adding them the sum will be +3y - 3y = 0
so y will be got eliminated
so, add both the equation,
x + 3y + 2x - 3y = 5 + 1
x + 2x + 0 = 6
3x = 6
x = 6/3
x = 2
now put x = 2 in equation x + 3y = 5
2 + 3y = 5
3y = 5 - 2
3y = 3
y =3/3
y = 1
so the answer is (2, 1)