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 plus 5 x second row y equals 10 plus 3 x 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=−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

Answer 1

To represent the situation described, we need to write equations that model the height of the egg as it falls over time. Since the eggs are dropped from a height of 10 feet, this height decreases as time passes.

1. The first egg falls at a rate of 5 feet per second. The height of the egg over time \( x \) seconds can be represented as:
\[
y = 10 - 5x
\]
This means that for every second \( x \), the height \( y \) decreases by 5 feet from the initial height of 10 feet.

2. The second egg falls at a rate of 3 feet per second. Its height can be represented as:
\[
y = 10 - 3x
\]
Similarly, for this case, the height \( y \) decreases by 3 feet for each second \( x \).

Putting these together, the system of equations that represents the situation is:
\[
\begin{align*}
y &= 10 - 5x \\
y &= 10 - 3x
\end{align*}
\]

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