Warm-up:

1. You will need a ruler today!

2. Complete the Warm-up in your notes.

Homework:

Quiz 1.3

Standard 1.4:

solve systems of equations (2-1, 2-2)

In these sections we will…

Solve systems of equations involving two variables algebraically.

Solve systems of equations involving three variables algebraically.

What does the solution for a system of linear equations represent?

Is (3,5) a solution for the given system?

8

4 7

y x

y x

How Can We Solve a System?

Graphing

Elimination

Substitution

Solve the following systems by graphing:

1. 2

3 10

2. 3 0

2 6 5

x y

x y

x y

x y

Let’s check on the calculator!

Substitution and Elimination:

1. 5 16

2 3 3

2. 35 40 55

7 8 11

x y

x y

x y

x y

Let’s check on the calculator!

Word Problem!

p 71 #10 Sales – HomePride manufacturers solid oak racks

for displaying baseball equipment and karate belts.

They usually sell six times as many baseball racks

as karate belt racks. The net profit is $3 from each

baseball rack and $5 from each karate belt rack. If

the company wants a total profit of $46,000, how

many of each type of rack should they sell?

Solving Systems in 3 Variables

A system in 3 variables represents the intersection of 3 planes.

p 73.

Solving…

Graphing is too complex forget it.

Must have the same number of equations as you have variables.

Use substitution or elimination repeatedly!

What kind of solutions?

Unique Solution (x,y,z): ordered triple, problem solves to give a value for all 3 variables

Infinite solutions:

No Solution:

Let’s try some…

3 9

4 2 2 0

3 4 2

y z

x y z

x y z

How should the solution be written?

3 7 14

5 3 2 3

2 4 7

x y z

x y z

x y z

Example 2:

P 76 #7

Now…YOU think – talk with your group!

Write a system of 3 equations that fits each description.

The system has a solution of x = - 5, y = 9 and z = 11.

There is no solution to the system.

The system has an infinite number of solutions.

Homework:

HW1 1.5: P 71 #22 – 25 all

HW2 1.5: P 76 #9, 11 and 13

UNIT 1 Test