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 \(x\).
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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.
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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: \[ {y = 10 - 5x, y = 10 - 3x} \]