Question

Writing Simultaneous Linear Equations Quick Check
5 of 55 of 5 Items












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 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

Answer 1

To represent the situation described in the problem, we need to write equations for the height of the egg as a function of time based on the fall rate of each design.

1. The first student's egg design causes the egg to fall at a rate of 5 feet per second. If the initial height is 10 feet, the height \( y \) after \( x \) seconds would be:
\[
y = 10 - 5x
\]

2. The second student's egg design causes the egg to fall at a rate of 3 feet per second. Similarly, the height \( y \) after \( x \) seconds would be:
\[
y = 10 - 3x
\]

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

This matches the third option in your responses:
\[
\{y = 10 - 5x, y = 10 - 3x\}
\]