Question 471925
The unstated assumption in the question is that the ordered pair is written as (x, y) and not (y, x). 
With this assumption we can then see that by giving the ordered pair (_, 78), the author of the question wants us to understand that y = 78 and x is not known. 
However, x can be found from the fact that y = 78 and the fact that the two variables are related through the equation:
y = -10x + 18.
Substituting y = 78 into the equation we can find the value of x.
78 = -10x + 18
Take away 18 from both sides of the equation (the purpose is to isolate x on one side).
78 - 18 = -10x + 18 - 18
Simplify.
60 = -10x,
which is the same as
-10x = 60
Divide the whole equation by -10 (the purpose is still the same: isolate a single x to be alone on one side of the equation)
-10x/(-10) = 60/(-10)
Simplify
x = -6
Solved.
The ordered pair is (-6, 78)