Will upvote!
which ordered pair is the solution to the system of equations?

{2x−y=−5
{x+3y=22

(7, 19)
(4, 9)
(8, 21)
(1, 7)

Just "plug n chug" as my teacher would say. In other words, replace the letters with the values. 

Choice A is (7,19) which means x = 7 and y = 19. Let's replace the x and y value with these numbers in both equations. If we get a true equation, then we found the answer. 

2x-y = -5
2*7-19 = -5
14-19 = -5
-5 = -5 ... true
So that works. Let's try the other equation
x+3y = 22
7+3*19 = 22
7+57 = 22
64 = 22 ... false 
So choice A is NOT the answer because of this. Let's try out choice B
2x-y = -5
2*4-9 = -5
-1 = -5 ... false
so B doesn't work either. How about C? 
2x-y = -5
2*8-21 = -5
-5 = -5 ... that works
x+3y = 22
8+3*21 = 22
71 = 22 ... but this is false
So D has to be the answer. Let's check to confirm or not
2x-y = -5
2*1-7 = -5
-5 = -5 ... true
x+3y = 22
1+3*7 = 22
22 = 22 ... true
BOTH equations are true at the same time so (1,7) is definitely the final answer

Where's the rest of the