We are given that:
Lashonda rented 3 movies and 2 video games for a total of $19. If "x" is the cost per movie and "y" the cost per video game, then we can write this mathematically as:

This is our first equation.
We are also given that:
She rented 5 movies and 6 video games for a total of $47. This can be written mathematically as:

This is our second equation.
To solve the system we will solve for "x" in equation (1). To do that we will subtract "2y" from both sides:

Now we divide both sides by 3:

Now we substitute this in equation (1):

Now we use the distributive law on the parenthesis:

Now we multiply both sides by 3, we get:

Now we add like terms:

Now, we subtract 95 from both sides:

Dividing both sides by 8:

Now we substitute this value in equation (1), the one where we have solved for "x", we get:

Solving the operations we get:

Therefore, each movie costs $2.5 and each video game costs $5.75.