Today’s Agenda

Attendance / Announcements

Collect Projects

Return Exams

Sections 6.1, 6.2

Quiz Friday

Exam Schedule

Exam 4 (Ch 6,7)

Fri 11/15

Exam 5 (Ch 10)

Thur 12/5

Final Exam (All)

Thur 12/12

Review: Graphing/Equations of

Lines

Sections 2.1, 2.2

Systems of Linear Equations

A solution of a system of linear

equations is an ordered pair that

satisfies both equations.

12

93

yx

yx

Solve by Graphing

12

93

yx

yx

So, the

solution of

the system

is (2, -3)

Solve by Graphing

2

842

21 xy

yx

So, the

solution of

the system

is ?

Solve by Graphing

642

32

yx

yx

So, the

solution of

the system

is ?

Solve by Graphing

Solving Systems Algebraically

The Substitution Method

• Works well when it is easy to solve

for one of the variables

• Substitute expression into other

equation, Solve.

• Plug solved value back into either

equation to find solution.

• Check the solution in both equations

The Substitution Method

2356

63

yx

yx

• What does this tell us about the

graphs of the system?

The Substitution Method

762

93

xy

yx

• What does this tell us about the

graphs of the system?

The Substitution Method

428

24

yx

yx

• What does this tell us about the

graphs of the system?

The Substitution Method

52

32

yx

yx

• What does this tell us about the

graphs of the system?

Solving Systems Algebraically

The Elimination Method

• We can multiply/divide any linear

equation.

• We can also add/subtract linear

equations together.

• Use algebra to eliminate one of the

variables, solve for the other.

• Check the solution in both equations

The Elimination Method

123

45

yx

yx

Addition Method

- Want to get

“opposite

coefficients”

- Then add

equations to

eliminate variable

Subtraction

Method

- Want to get

“same

coefficients”

- Then subtract

equations to

eliminate variable

The Elimination Method

1232

232

xy

yx

Want to rewrite to line up like

terms

The Elimination Method

267

1452

yx

yx

Applications

The sum of two numbers is 70 and

their difference is 24. Find the two

numbers.

Solving Larger Systems using

Substitution

• Use algebra to isolate one of the

variables, substitute into the other

two.

• Solve the two variable system, use

Substitution find the first variable

• Check solution in all three equations

The Substitution Method

2

123

22

zyx

zyx

zyx

The Substitution Method

723

164

232

zyx

zyx

yx

The Substitution Method

2242

22

52

zyx

zyx

zyx

Classwork / Homework

• Page 317

•1 – 15 odd, 19

• Page 329

•9, 39, 41, 45