Which ordered pair (a, b) is a solution to the given system?

Since you are given a list of choices, you can go through each choice to plug them into the equations. It turns out that choice B is the answer

(3,1) means that a = 3 and b = 1
Plug in a = 3 and b = 1 into the first equation
2a - 5b = 1
2*3 - 5*1 = 1 replace 'a' with 3, replace b with 1
6 - 5 = 1
1 = 1
we get a true equation, so we have confirmed the first equation

Do the same for the second equation
3a+5b = 14
3*3+5*1 = 14 replace 'a' with 3, replace b with 1
9+5 = 14
14 = 14
we get a true equation, so the second equation has been confirmed

Both equations are true when (a,b) = (3,1). So the answer (3,1) has been confirmed fully