Write a system of linear equations that has the ordered pair as its solution (3,5)

An easy way to do this is by using the simplest equations you can:

x + y and x - y

(3, 5) is (x, y). all you have to do is plug those into your equations and get a result, so:

x + y = 8
(because 3 + 5 = 8)
x - y = -2
(because 3 - 5 = -2)

and those can serve as your system of equations. 

you can check it by solving by substitution:
x - y = -2
x + y = 8

solve one of the equations for a single variable:
x = y - 2

plug it into the second equation:
(y - 2) + y = 8
y - 2 + y = 8
2y - 2 = 8
2y = 10
y = 5

then plug that result back into the equation:
x + y = 8
x + 5 = 8
x = 3