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

1 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

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

3 {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

4 {y=10−5xy=10−3x

Answer 1

To represent the situation described for the parachute designs in an egg-drop project, we need to determine how the height \(y\) changes with respect to time \(x\).

Both eggs are dropped from an initial height of 10 feet.

1. The first design causes the egg to fall at a rate of 5 feet per second. Thus, the height of the egg at time \(x\) seconds can be described by the equation: \[ y = 10 - 5x \]

2. The second design causes the egg to fall at a rate of 3 feet per second. Therefore, the height of that egg at time \(x\) seconds can be represented with the equation: \[ y = 10 - 3x \]

Combining these two equations into a system, we have:

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

Thus, the correct choice from the provided options is:

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