Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Hakim received some gift cards for music and movie downloads for his birthday. Using one of them, he downloaded 20 songs and 13 movies, which cost a total of $163. Using another, he purchased 13 songs and 13 movies, which cost a total of $156. How much does each download cost?

Downloads cost $for a song and $ for a movie.

the download cost for a song is $1 and $11 for a movie

Step-by-step explanation:

According to the questions, the following equations are as follows:

Let us assume the song be x

And, the movies be y

So,

20x + 13y = $163(i)

13x + 13y = $156(ii)

Now solve substract second equation from the first equation

7x = $7

x = $1

And the y value is

20 + 13y = $163

13y = $163 - $20

13y = $143

y = $11

Hence, the download cost for a song is $1 and $11 for a movie

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."