Let x represent the rental cost for each movie.
Let y represent the rental cost for each video game.
From the information given,
Lamar rented 3 movies and 8 video games for a total of $58. The equation representing this scenario would be
3x + 8y = 58
Also,
he rented 5 movies and 2 video games for a total of $23. The equation representing this scenario would be
5x + 2y = 23
We would solve both equations by applying the method of elimination. To elimimate x, we ould multiply the first equation by 5 and the second equation by 3. We have
15x + 40y = 290
15x + 6y = 69
Subtracting the second equation from the first, we have
15x - 15x + 40y - 6y = 290 - 69
34y = 221
Dividing both sides by 34,
34y/34 = 221/34
y = 6.5
Substituting y = 6.5 into 5x + 2y = 23, we have
5x + 2(6.5) = 23
5x - 13 = 23
Adding 13 to both sides, we have
5x - 13 + 13 = 23 - 13
5x = 10
x = 10/5
x = 2
Rental cost for each movie = $2
Rental cost for reach video = $6.5