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Agenda for Thur sday 11 /29 / 12PowerPoint Presentation

Agenda for Thur sday 11 /29 / 12

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Agenda for Thur sday 11 /29 / 12

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Target 7a: I can solve linear systems by graphing,

substitution, and elimination.

- Questions on solving using substitution
- More on Solving Linear Systems Using Substitution
- Assignment…

Solving Linear Systems

Using Substitution

Solving Linear Systems Using Substitution

x = 2y – 6

x – 2y = -6

4x + 6y = 4

Before you can use substitution, x or y needs to be

alone in one of the equations.

4(2y– 6) + 6y = 4

8y – 24 + 6y = 4

14y – 24 = 4

+24 +24

14y = 28

14 14

y = 2

Plug 2y – 6 in for x.

Solve for y.

x = 2(2) – 6

x = -2

Plug 2 in for y.

Solve for x.

The solution is (-2,2)

Lets try another one together!

y = -5x – 12

-5x – y = 12

3x – 5y = 4

Get x or y alone in one of the equations.

3x – 5(-5x– 12) = 4

3x + 25x + 60 = 4

28x + 60 = 4

-60 -60

28x = -56

28 28

x = -2

y = -5(-2) – 12

y = -2

Plug -5x – 12 in for y.

Solve for x.

Plug -2 in for x.

Solve for y.

The solution is (-2,-2)

Try these…

x = y + 3

x – y = 3

x + 2y = -6

y = -3x – 7

3x + y = -7

-2x + 4y = 0

(y + 3) + 2y = -6

3y + 3 = -6

-3 -3

3y = -9

3 3

y = -3

x = -3 + 3

x = 0

(0,-3)

-2x + 4(-3x – 7) = 0

-2x – 12x – 28 = 0

-14x – 28 = 0

+28 +28

-14x = 28

-14 -14

x = -2

y = -3(-2) – 7

y = -1

(-2,-1)

A Word Problem!

Last year, you mowed grass and shoveled snow for 12

households. You earned $225 for mowing a household’s

lawn for an entire year and $200 for shoveling a household’s

walk and driveway for an entire year. You earned a total of

$2600 last year. How many households did you mow and

shovel for last year?

Step 1: Write a system of equations.

x is mowing

y is shoveling

x + y = 12

225x + 200y = 2600

y = -x + 12

Step 2: Solve using substitution.

225x + 200(-x + 12) = 2600

225x – 200x + 2400 = 2600

25x + 2400 = 2600

25x = 200

x = 8

y = -8 + 12

y = 4

8 lawns mowed

4 walks & driveways

shoveled

Target 7a: I can solve linear systems by graphing,

substitution, and elimination.

- Assignment…
- Pg. 439-440