Warm-up• Solve the first system of equations by the

Substitution Method, then graphing

3 16

2 3 4

x y

x y

(4, 4)

1. (6, 1)

2. (4,4)

3. (2,1)

4 24. ( , )

3 3

6. ( 10,6)

5. No Solution

7. : $450 : $100

4

50 20 550

E A

E A

E A

8. 4 5

9

479 339 3611

Electric Acoustic

E A

E A

Solving Linear Systems Algebraically with Elimination

Section 3-2

Pages 160-1-67

Objectives

• I can use the elimination method to solve equations

• I can set up and solve word problems using elimination

Elimination Method

• GOAL

• 1. Add the equations together and have one variable term go away.

• 2. Sometimes you will have to multiply one or both equations by a number to make this happen.

Example 1

3 2 6

4 2 8

x y

x y

7 14x

2x Now, PLUG this back intoEither equation to find “y”

3(2) 2 6y

6 2 6y 2 0y

0y

(2,0)

What does this mean?

• Remember that a solution to a system of equations is where the graphs cross

• It is ALWAYS an Ordered Pair

Multiplying by a number?

• Many times you cannot add the equations and have a variable term cancel

• For these cases, you must multiply One or Both equations by a number first

• Let’s look at a few

What to Multiply by?45

932

yx

yx

)45(2

)932(5

yx

yx

)45(3

)932(

yx

yx

x-variable will cancel

y-variable will cancel

Example 23 5 4

2 3 29

x y

x y

2(3 5 4)

3(2 3 29)

x y

x y

6 10 8

6 9 87

x y

x y

19 95y

5y

2 3( 5) 29x

2 15 29x

2 14x

7x

(7, 5)

Your Turn

• Solve the following system of equations using elimination:

2932

1127

yx

yx)9,1(: Solution

Other Methods

• Remember, the solution to a system of equations if an ordered pair

• You know 2 other methods to check your answers:– Graphing Calculator and asking for the

intersection (2nd, Trace, Intersection, E, E, E)– Substitution Method

Solution Types

Remember there are 3 types of solutions possible from a system of equations!

No Solution vs Infinite

• How will you know if you have No Solution or Infinite Solutions when solving by Substitution??

Remember Back to Solving Equations

No Solution• Variables are gone and

you get this:

• 2x + 3 = 2x – 4• 3 = -4• This is not possible, so

• No Solution

Infinite Solutions• Variables are gone and

you get this:

• 2x + 3 = 2x + 3• 3 = 3• This is always true, so

• Infinite Solutions

Word Problems

• When solving a word problem, consider these suggestions

• 1. Identify what the two variables are in the problem

• 2. Write equations that would represent the word problem, looking for key words

• Sum, difference, twice, product, half, etc…

Example 1

• GEOMETRY: The length of a rectangle is 8 cm more than twice the width. If the perimeter is 40 cm, find the dimensions.

Variables:

Length (L)

Width (W)

Equations:

L = 2W + 8

2L + 2W = P

Now, solve by elimination

Example 2

• Rental car agency A charges $8 per day plus $.20 per mile. Rental car company B charges $10, but only $.10 per mile. At what mileage is it better to use Company B?

Cost (C)

Miles (M)

Equations:

C = 8 + .20M

C = 10 + .10M

Now, solve by Elimination

Homework

• Elimination Worksheet