Question

The equations represent the heights, y, of the flowers, in inches, after x days. Which ordered pair, (1,2.7),(1,2.4), or (0,2), is a solution to the system? Will the flowers ever be the same height? Explain

Answer 1

The ordered pair (1,2.4) is a solution to the system of equations, and the flowers will not be the same height.

Step-by-step explanation:

The system of equations represents the heights (y) of flowers in inches after a certain number of days (x). Let's evaluate the ordered pairs (1,2.7), (1,2.4), and (0,2) to determine which one is a solution to the system.

For the first ordered pair (1,2.7):

`\[y_1 = 3(1) - 0.3(1)^2 = 2.7\]`

The calculated value matches the given height of 2.7 inches, so (1,2.7) is a solution.

For the second ordered pair (1,2.4):

`\[y_2 = 3(1) - 0.3(1)^2 = 2.7\]`

The calculated value does not match the given height of 2.4 inches, so (1,2.4) is not a solution.

For the third ordered pair (0,2):

`\[y_3 = 3(0) - 0.3(0)^2 = 0\]`

The calculated value matches the given height of 2 inches, so (0,2) is a solution.

Now, addressing whether the flowers will ever be the same height, we observe that the ordered pairs (1,2.7) and (0,2) are solutions to the system, and their respective heights are different. Therefore, the flowers will not be the same height. This conclusion is based on the specific values plugged into the equations and demonstrates the different growth rates or starting points for the flowers.

Answer 2

Which ordered pair is a solution to the system of equations representing the heights of flowers over time, substitute the values of x and y from each ordered pair into the equations. If the values on both sides of each equation are equal, then the ordered pair is a solution to the system. If there is a solution to the system, the flowers will be at the same height at that particular time.

You have three ordered pairs: (1,2.7), (1,2.4), and (0,2). To determine which one is a solution to the system of equations representing the heights of flowers over time, you need to substitute the values of x and y from each ordered pair into the equations. If the values on both sides of each equation are equal, then the ordered pair is a solution to the system. You need to perform similar substitutions for the other two ordered pairs. Regarding whether the flowers will ever be the same height, you'll need to check if the system of equations has a solution (an intersection point). If there is a solution, it means the flowers will be at the same height at that particular time. If there is no solution, it implies that the flowers will not be at the same height.