Question

Use the elimination method to solve the system of equations. Choose the correct ordered pair. 

5x + 3y = 58
5x - 3y = 22

Answer 1

5x+3y=58
5x-3y=22
(3y gets cancelled bc 3y-3y=0,  then add 5x with 5x, so you're left with)
10x=80, (divide both sides by 10)
x=8
Now we look for y. So choose one formula from the two (let's say 5x + 3y=58)
Substitute x for 8 so it will look like---- 5(8)+3y=58
Multiply 5*8--- so you get --  40+3y=58
Subtract 40 from both sides and you're left with 3y=18
divide both sides by 3
you get y=6
In conclusion, x=8 and y=6 hence, (8,6)

Answer 2

Subtract 2nd equation from 1st, in order to eliminate x from the expression, 
6y = 36
y = 36/6
y = 6

Now, Substitute it in 1st equation,
5x + 3(6) = 58
5x = 58 - 18
x = 40 / 5
x = 8

In short, Your Answer would be Option A) (8, 6)

Hope this helps!