## Algebra 1: Common Core (15th Edition)

Published by Prentice Hall

# Chapter 6 - Systems of Equations and Inequalities - 6-2 Solving Systems Using Substitution - Practice and Problem-Solving Exercises - Page 375: 24

#### Answer

There were 2 buses and 4 vans.

#### Work Step by Step

Set up two equations: x+y=6 and 51x+10y=142. X represents the buses and the Y represents the cars. Isolate the y in the first equation in order to be able to substitute it into the first equation: x+y=6 -subtract x from both sides- y=6-x Substitute the equation into the second equation: 51x+10y=142 -substitute- 51x+10(6-x)=142 -distribute- 51x+60-10x=142 -simplify like terms- 41x+60=142 -subtract 60 from both sides- 41x=82 -divide both sides by 41- x=2 Substitute x=2 into one of the equations: 2+y=6 -subtract 2 from both sides- y=4 Check the solution: 51x+10y=142 51(2)+10(4)=142 102+40=142 142=142 There were 2 buses and 4 vans.

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