Question

four friends plan to meet at the top of the eiffel tower. each arrives about the time the tower opens and starts climbing the stairs to the top. the graphs show the number of stairs each has climbed, s, in the m minutes since the tower opened. tell how many solutions each system has. what does each solution mean in this context?

a.

b.

Explanation:

Part a: Jayden and Elizabeth

Step 1: Analyze the Graphs

The graphs for Jayden (red) and Elizabeth (blue) are two lines that intersect at one point. In a system of linear equations (where each line represents the relationship between minutes \( m \) and stairs climbed \( s \) for each person), the intersection point is the solution.

Step 2: Interpret the Solution

The intersection means there is one solution. In context, this solution represents the time \( m \) (in minutes after the tower opened) when Jayden and Elizabeth have climbed the same number of stairs \( s \). At that specific time, they are at the same position on the stairs (same number of stairs climbed).

Part b: Pala and Mel

Step 1: Analyze the Graphs

The graphs for Pala (blue) and Mel (red) are two parallel lines. Parallel lines have the same slope and never intersect.

Step 2: Interpret the Solution

Since parallel lines do not intersect, the system of equations (representing their stair - climbing progress) has no solutions. In context, this means there is no time \( m \) (in minutes after the tower opened) when Pala and Mel have climbed the same number of stairs \( s \); their rates of climbing stairs are such that they will never be at the same number of stairs climbed at the same time.

Answer:

• Part a: The system (Jayden and Elizabeth) has 1 solution. This solution means there is a specific number of minutes after the tower opened when Jayden and Elizabeth have climbed the same number of stairs.
• Part b: The system (Pala and Mel) has 0 solutions. This means there is no time after the tower opened when Pala and Mel have climbed the same number of stairs.