20 pts and a one month mai rented 5 movies and 3 video games for a total of $22. the next month she rented 2 movies and 6 video games for a total of $34. find the rental cost for each movie and each video game.

Step-by-step explanation:

Let m and v represent the rental costs of movies and video games, respectively. The two rentals can be described by the equations ...

  5m +3v = 22

  2m +6v = 34

We notice that the coefficient of v in the second equation is 2 times that in the first equation. This will make it easy to eliminate v as a variable.

Subtracting the second equation from 2 times the first gives ...

  2(5m +3v) -(2m +6v) = 2(22) -(34)

  8m = 10 . . . . . . . . . . . simplify

  m = 10/8 = 1.25 . . . . . divide by the coefficient of m

Using this in the second equation, we can find v:

  2(1.25) +6v = 34 . . . . .substitute for m

  6v = 31.50 . . . . . . . . . subtract 2.50

  v = 5.25 . . . . . . . . . . . divide by the coefficient of v

The rental cost for a movie is $1.25; for a video game it is $5.25.