One month juan rented 6 movies and 5 video games for a total of $44 . the next month he rented 2 movies and 3 video games for a total of $22 . find the rental cost for each movie and each video game.

Let m = movies, let v = video games. 

6m + 5v = 44
2m + 3v = 22

Multiply the first equation by 3 and the second equation by - 5

18m + 15v = 132
- 10m - 15v = - 110

Notice, the v-variables cancel each other out. Combine like terms, you are left with:

8m = 22

Divide both sides by 8. 
m = 2.75

Plug this into either equation to solve for V. 

2(2.75) + 3v = 22
5.50 + 3v = 22
3v = 22 - 5.50
3v = 16.50
Divide both sides by 3 to isolate variable v. 

v = 5.50

Movies cost $2.75 and video games cost $5.50.