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MyMathLabs HW Due Sunday

Section 6.1, 6.2

Exam Schedule

Exam 5 (Ch 6.1, 7)

Wed 4/1

Exam 6 (Ch 10)

Monday 4/27

Final Exam (Cumulative)

Monday 5/4

Review: Graphing/Equations

of Lines

Sections 2.1, 2.2

Linear Equations

How can we solve this?

93 yx

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

123

45

yx

yx

The Elimination Method

1232

232

xy

yx

Want to rewrite to line up like terms

The Elimination Method

267

1452

yx

yx

Solving for three unknowns using

back substitution

2𝑥 − 𝑦 + 3𝑧 = 2𝑥 + 2𝑦 − 𝑧 = 6

−𝑥 − 𝑦 + 𝑧 = −5

Graphing Linear Inequalities

Graphing Linear Inequalities

𝑦 < 𝑥 + 3

1. Graph boundary line

3 xy

2. Check inequality sign

(Dashed or Solid?)

3. Shade accordingly

4. Test Points

Graphing Linear Inequalities

1. Graph boundary line

2

3

2

1 xy

2. Check inequality sign

(Dashed or Solid?)

3. Shade accordingly

4. Test Points

624 xy 23

21 xy

Classwork / Homework

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•1 – 15 odd, 19, 26

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