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The two high schools, Jeff erson Hills East and Jeff erson Hills West, are taking fi eld trips to the state capital. A total of 408 students from Jeff erson Hills East will be going in 3 vans and 6 buses. A total of 516 students from Jeff erson Hills West will be going in 6 vans and 7 buses. Each van has the same number of passengers and each bus has the same number of passengers. a. Write a system of equations that represents this problem situation. Let x represent the number of students in each van, and let y represent the number of students in each bus. b. How are the equations in the system the same? How are they diff erent? c. Describe the fi rst step needed to solve the system using the linear combinations method. Identify the variable that will be eliminated as well as the variable that will be solved for when you add the equations. d. Solve the system of equations using the linear combinations method. Show your work. e. Interpret the solution of the linear system in terms of t

 Jan 12, 2021
 #1
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3x +  6y  =   408

6x +  7y  =    516

 

 

Eliminate  x

Multiply the first equation through  by   -2

 

-6x  - 12y  =  - 816

6x  +  7y  =     516           add these

 

 

-5y  =  -300    divide both sides by -5

 

y = 60 =    stidents  in each bus

 

3x + 6(60)  = 408

 

3x  +  360  =  408      subtract  360  from both sides

 

3x =  48     divide  both sides by  3

 

x = 16  =  students in each van

 

 

cool cool cool

 Jan 12, 2021

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