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=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 minus 5 x second row y equals 10 minus 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=−5xy=−3x

Answer 1

To represent the situation described, we need to establish a relationship between the height \( y \) of the egg and the time \( x \) it has been falling, based on the rates at which the eggs fall.

1. **First Student (falling at a rate of 5 feet per second)**:
- The egg starts at a height of 10 feet, and as time \( x \) increases, the height decreases at 5 feet per second.
- The equation for this would be:
\[
y = 10 - 5x
\]

2. **Second Student (falling at a rate of 3 feet per second)**:
- Similarly, this egg also starts at a height of 10 feet but decreases at a rate of 3 feet per second.
- The equation for this would be:
\[
y = 10 - 3x
\]

Thus, the system of equations that represents the situation is:
\[
\begin{cases}
y = 10 - 5x \\
y = 10 - 3x
\end{cases}
\]

This matches the option:
\({y=10−5x \, y=10−3x} \)

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