Applications of Systems Skill 43

Objective HSA-REI.6(2): Solve systems of linear equations exactly and approximately, with graphs, focusing on pairs of linear equations in two variables.

Example, solve using systems The state fair is a popular field trip destination. This year Sheldon and the Riverside both planned trips there. The Sheldon rented and filled 8 vans and 8 buses with 240 students. Riverside rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. a) Write a system of equations describing the situation. Sheldon: 8v + 8b = 240 Riverside: 4v + 1b = 54 𝟖𝒗+𝟖𝒃=𝟐𝟒𝟎 𝟒𝒗+𝟏𝒃=𝟓𝟒

Example, solve using systems b) Solve the system of equations. 8𝑣+8𝑏=240 4𝑣+1𝑏=54 (-8) 4𝑣+1𝑏=54 8𝑣+8𝑏=240 −32𝑣−8𝑏=−432 4 8 +𝑏=54 + 32+𝑏=54 −24𝑣=−192 𝑏=22 𝑣=8 There are 8 people per van and 22 people per bus.

Example, solve using systems Find the value of two numbers if their sum is 12 and their difference is 4. a) Write a system of equations describing the situation. 𝑥+𝑦=12 𝑥−𝑦=4 b) Solve the system of equations. + 𝑥+𝑦=12 2𝑥=16 8 +𝑦=12 𝑥=8 𝑦=4 The bigger number is 8 and the smaller number is 4.

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