1)) Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. ()) One Friday night, two large groups of people called Silvergrove Taxi Service. The first group requested 2 sedans and 1 minivan, which can seat a total of 11 people. The second group asked for 3 sedans and 2 minivans, which can seat a total of 19 people. How many passengers can each type of taxi seat? S) A sedan can seat Save answer

Let \( s \) represent the number of passengers a sedan can seat and \( m \) represent the number of passengers a minivan can seat. Based on the given information, we can create the following system of equations: 1) \( 2s + m = 11 \) (from the first group's request) 2) \( 3s + 2m = 19 \) (from the second group's request) Now, let's solve the system of equations. From the first equation, we can express \( m \) in terms of \( s \): \[ m = 11 - 2s \] Substituting this expression for \( m \) into the second equation: \[ 3s + 2(11 - 2s) = 19 \] Expanding and simplifying: \[ 3s + 22 - 4s = 19 \] \[ -s + 22 = 19 \] \[ -s = 19 - 22 \] \[ -s = -3 \] \[ s = 3 \] Now, substituting \( s = 3 \) back into the expression for \( m \): \[ m = 11 - 2(3) = 11 - 6 = 5 \] So, a sedan can seat **3 passengers**, and a minivan can seat **5 passengers**. Here are the fun facts: Did you know? The first commercial taxi service was established in Paris in 1899 using gasoline-powered cabs! These early taxis transformed public transportation, making it more accessible and paving the way for modern taxi services like Uber and Lyft we rely on today. If you're ever in a pinch solving equations, try graphing them! It’s like visualizing a friendly dance where each line represents a group of partners meeting at the dance floor. Just find where they overlap, and you've got yourself a solution!