3.2 (day 1) Solving Systems

AlgebraicallyObjective: To solve linear systems of

equations using the substitution method.

• In preparation for the annual Academic Banquet, Mrs. Plesniak and the IHS student council must plan out the number and types of tables needed to accommodate 200 honorees and guests. Rectangular tables can seat 8 people and round tables can seat 6 people. They can afford to rent 30 tables. How many of each table should they rent for the banquet?

Steps for Substitution• Solve one equation for one of the variables• Substitute expression into other equation• Solve• Substitute answer into first equation• Write your answer as an ordered pair

Example 1

{2𝑥−3 𝑦=6𝑥+𝑦=−12

Example 2

{ 3 𝑥− 𝑦=04 𝑥+3 𝑦=26

Example 3

{ 𝑥+3 𝑦=12−2 𝑥+4 𝑦=9

Questions• What do you think you would get as an answer if

there were no solutions?

• What do you think you would get as an answer if there were infinite solutions?

Homework• Page 126 #1-12, 52,54