Question

genesis starts at the 30th step and climbs up 15 steps each minute.how many solutions does this system of equations have?infinitely many solutionsthe system has infinitely many solutions because genesis and esme will always be on the same step at the same time.find three ordered pairs that are solutions to this system of equations.(2, 60) (2, 45) (3, 60)(1, 45) (3, 75) (1, 30)

Explanation:

Step1: Define Genesis's step function

Let $t$ = time in minutes, $s$ = step number. Genesis starts at step 30, climbs 15 steps/min:
$$s = 30 + 15t$$

Step2: Verify ordered pairs

Check which pairs $(t,s)$ satisfy $s=30+15t$:

• For $(1,45)$: $30+15(1)=45$, valid.
• For $(2,60)$: $30+15(2)=60$, valid.
• For $(3,75)$: $30+15(3)=75$, valid.

Answer:

$(1, 45)$, $(2, 60)$, $(3, 75)$