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)

Question

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

Answer 1

To represent the situation described, we need to find equations that correctly express the height of the egg as it falls over time.

For each student, the egg is dropped from an initial height of 10 feet. The rate of fall is different for each design.

1. The first design falls at a rate of 5 feet per second. Therefore, for this design, the height \( y \) after \( x \) seconds can be expressed as:

   \[ y = 10 - 5x \]

This equation indicates that for every second that passes, the egg drops by 5 feet.

2. The second design falls at a rate of 3 feet per second. Therefore for this design, the height \( y \) can be expressed as:

   \[ y = 10 - 3x \]

This reflects that for every second that passes, the egg drops by 3 feet.

Thus, the system of equations representing both designs is:

\[ \begin{cases} y = 10 - 5x \ y = 10 - 3x \end{cases} \]

So the correct choice from the options provided is:

\[ { y = 10 - 5x, y = 10 - 3x } \]