Question

Question

Two students were testing the parachute designs they made for an egg-drop project. Both students dropped their eggs from a height of 10 feet. One design made the egg fall at a rate 5 feet per second, and the other design made the egg fall at a rate of 3 feet per second. If x represents the time in seconds that the egg falls and y represents the height of the egg, which system of equations represents the situation described?(1 point)
Responses

{y=10−5xy=10−3x
enlarged left brace start layout first row y equals 10 minus 5 x second row y equals 10 minus 3 x end layout

{y=−5xy=−3x
enlarged left brace start layout first row y equals negative 5 x second row y equals negative 3 x end layout

{y=10+5xy=10+3x
enlarged left brace start layout first row y equals 10 plus 5 x second row y equals 10 plus 3 x end layout

{y=5x−10y=3x −10

Answer 1

To represent the situation described with a system of equations, we need to model the height of the egg (y) as it falls over time (x).

1. The first student’s egg falls at a rate of 5 feet per second from an initial height of 10 feet. Therefore, its height over time can be represented as: \[ y = 10 - 5x \]

2. The second student’s egg falls at a rate of 3 feet per second from the same initial height of 10 feet, represented as: \[ y = 10 - 3x \]

Putting both equations together, we have the system of equations: \[ \begin{cases} y = 10 - 5x \ y = 10 - 3x \end{cases} \]

So the correct response is: \[ {y = 10 - 5x, y = 10 - 3x} \]