. Write a system of linear equations that represent this situation.

Question

You downloaded 2dvds and 10 songs for $18. Your friend downloaded 3dvds and 15 songs for $27. Write a system of linear equations that represent this situation. Can you determine the price of each DVD and each song? Explain

Answer 1

Price for downloading a dvd = x

Price for downloading a  a song =y

 

You downloaded 2dvds and 10 songs for $18.

2x + 10y = 18 _____ eq 1

 

Your friend downloaded 3dvds and 15 songs for $27

3x +15 y= 27____ eq 2

 

these are system of linear equation.

If you solve system of linear equation you can determine price of each dvd and each song

Answer 2

Hi Hannah,

 

Let's say d = DVDs and s = songs.

 

We are given that 2d + 10s = 18 and that 3d + 15s = 27, since your friend downloaded 3 DVDs and 15 songs for $27. To answer the first instruction, what defines an equation, and specifically, a system of linear equations? I leave that to you to find out. If you would like me to confirm your answer, just comment and I'll get back to you.

 

Now to determine the price of one DVD and the price of one song, we can use the substitution:

 

10s = 18 - 2d   (I subtracted 2d from both sides.)

 

Let's plug it in to our second equation:

 

3d + 15s = 27   (We know simple algebra, right? 15s = 10s + 5s ... and 5s is one half of 10s)

 

3d + (18 - 2d) + (9 - d) = 27

 

Now let's solve for d:

 

0d = 0

 

Uh-oh! Did we do something wrong? No, we didn't. This just means that we are unable to determine the price of one DVD and one song without another equation or hint.

 

We could have seen this if you divided the first equation by 2 and the second equation by 3. You would then see that we were given the same equation twice. Because of that, d and s can have infinitely many solutions, since anything times 0 would always equal 0.

 

Hope this helps!