3-23-2Solving Linear Systems Solving Linear Systems

AlgebraicallyAlgebraically day 2day 2

Objective: CA 2.0: Students solve system of linear equations in two variables algebraically.

Example 5: 

Using a Linear System to Model

A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make?

Labels

People per pan = 14

Pans of pasta = P

People per tray = 6

Trays of sandwiches = S

People at the party = 64

Price per pan of pasta = 39

Pans of Pasta = P

Labels:

Price per sandwich tray = 12

Sandwich trays = S

Money to spend on food = 150

Equation 1: 14 6 64

Equation 2: 39 12 150

P S

P S

Linear Combination Method

28 12 128

38 12 150

11 22

2

P s

P s

P

P

Substitute the value P into one of the original equations

14p + 6s = 64

14(2) + 6s = 64

28 + 6s = 64

6s = 36

s = 6 The caterer should make 2 pans of pasta and 6 sandwich trays.

Home work page 152 33 –51 odd, 54 – 58 even, 67 – 81 odd