Solving a word problem using a system of linear equations of the form Ax + By = C

Question

One month Tammy rented 2 movies and 3 video games for a total of $23. The next month she rented 6

 movies and 5 video games for a total of $43. Find the rental cost for each movie and each video game.

Answer 1

Let's let X=the rental cost of a movie and Y=the rental cost of a video game

2x+3y=23

6x+5y=43

We can multiply both sides of the first equation by 3 and get

6x+9y=69

Then we can subtract one from the other

6x+9y=69

6x+5y=43

0x+4y=26

4y=26

y=6.5

Then we can put that 6.5 back into an equation

2x+3(6.5)=23

2x+19.5=23

2x=3.5

x=1.75