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=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=−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

Answer 1

To form the correct system of equations for the egg-drop project, we need to express the height of the egg \(y\) as a function of time \(x\).

1. For the first student, whose parachute design makes the egg fall at a rate of 5 feet per second, we can write the equation: \[ y = 10 - 5x \] Here, \(10\) is the initial height from which the egg is dropped, and \(5x\) represents the distance fallen after \(x\) seconds.

2. For the second student, whose parachute design makes the egg fall at a rate of 3 feet per second, the equation is: \[ y = 10 - 3x \] Similarly, \(10\) is the initial height, and \(3x\) is the distance fallen after \(x\) seconds.

Combining both equations, the system of equations representing the situation is: \[ \begin{cases} y = 10 - 5x \ y = 10 - 3x \end{cases} \]

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