Let

'x' be the cost of one popcorn, x > = 0

'y' be the cost of one soft drink, y > = 0

We need to find x and y.

Following the conditions we an write the following equations:

2*x + 3*y = 50

5*x + 7*y = 121

From the first equation we have

2*x = 50 - 3*y

x = (50 - 3*y) / 2

If we substitute for x in the second equation 5*x + 7*y = 121 we get

5*(50 - 3*y) / 2 + 7*y = 121

(250 - 15*y)/2 + 14*y/2 = 121 multiply both sides by 2

250 - 15*y + 14*y = 242

- 15*y + 14*y = 242 - 250

- y = - 8 multiply both sides by (-1)

y = $8

x = (50 - 3*8)/2 = (50 - 24)/2 = 26/2 = 13

x = $13

The cost of one popcorn is $13 and the cost of one soft drink is $8.