Question

One month Tammy rented

3
movies and
2
video games for a total of
$20
. The next month she rented
8
movies and
4
video games for a total of
$45
. Find the rental cost for each movie and each video game.

Answer 1

`3x + 2y = 20`

`8x + 4y = 45`

`where x = # of movies` and
`y = # of video games`

In order to solve this systems of equations problem, you need to use the elimination method.

You can multiply the top equation,
`3x + 2y = 20`, by -2 in order to eliminate the
`y` values.


`(3x + 2y = 20) *-2` will turn into
`-6x - 4y = -40`

From there, we can eliminate.


`-6x - 4y = -40`

`8x + 4y = 45`

Since
`4y` and
`-4y` are opposites in sign and equal in coefficients, we can remove them from our equations and add the rest of the terms together.


`-6x - 4y = -40`

`8x + 4y = 45`
will turn into -->

`2x = 5`

So, x =
`(5)/(2)`, which means 1 movie costs $2.50. Then, we can solve for the video game price,
`y`, by substituting our x back into one of the equations.


`3x + 2y = 20`

`3*<span>(5)/(2) </span>+ 2y = 20`

`y = (25)/(4)`

Each movie costs $2.50 and each video game costs $6.25.