Question 657343
You're off to a good start.  

Let x = liters of orange juice
and y = liters of prune juice.

Then x + y = 8.

Since each liter of orange juice costs $1.20 and each liter of prune juice costs $1.40, the total cost of the mixture is 1.20x + 1.40y.

We are given that the final drink costs $1.24 per liter, or $1.24*8 = $9.92 for the entire 8 liters.  This gives us our second equation:

1.20x + 1.40y = 9.92

We now have two equations in two unknowns:

x + y = 8
1.2x + 1.4y = 9.92

We'll use substitution.  From the first equation, move x to the right (by subtracting x from each side), giving 

y = 8 - x

Substituting for y in the second equation gives

1.2x + 1.4(8-x) = 9.92

Expanding:

1.2x + 11.2 - 1.4x = 9.92

Subtract 11.2 from each side and regroup:

(1.2x - 1.4x) = 9.92 - 11.2

Combining terms:

-0.2x = -1.28

Dividing both sides by -0.2:

x = -1.28/-0.2 = 6.4

From our first substitution, 

y = 8 - 6.4 = 1.6

So the final drink contains 6.4 liters of orange juice and 1.6 liters of prune juice.