Question

a class is on a field trip at the statue of liberty. luka starts... each minute. kellan starts at the 150th step and climbs down 15 steps each minute.\
(1) x: number of minutes\
y: number of steps\
(2) how many solutions does this system of equations have?\
one solution\
(3) what is the solution of the system of equations?\
(?, ?) with options 3, 5, 6, 8 for the first ?\
(chart: kellan: y = 150 - 15x, luka: y = 10x, axes: minutes (x), steps (y))

Explanation:

Step1: Set the equations equal

We have two equations: \( y = 10x \) (Lukas) and \( y = 150 - 15x \) (Kellan). To find the solution, set them equal: \( 10x = 150 - 15x \).

Step2: Solve for x

Add \( 15x \) to both sides: \( 10x + 15x = 150 \), which simplifies to \( 25x = 150 \). Then divide by 25: \( x = \frac{150}{25} = 6 \).

Step3: Find y

Substitute \( x = 6 \) into \( y = 10x \): \( y = 10 \times 6 = 60 \).

Answer:

\((6, 60)\)