Today:

Warm-Up (3)Systems of Inequalities (3)

Applying Systems of Equations (1)Class Work/Test Review

All Khan Academy Due Either Sunday Eve. or Monday During Class

Warm Up: (3)

2. What is the solution to the following system of equations:

2(m + n) + m = 93m - 3n = 24

Warm Up: A Note about Solving by Elimination

2 3 12

4 5 2

x y

x y

2) Make opposites.

3) Add and solve for the variable.

4) Substitute into ANY original equation.

1) Arrange the variables.

2y 3, 2

5) Check your answer.

11 22y 11 11

2 3 12x y

2 3 12x 2

6 6 2 6x 2 2

3x

4x 6y 244 5 2x y

2

2 6 12x

2 2

2x + 3y = 12-2 = 5y – 4x

Class Notes: Systems of Inequalities(3)

1. Write the equation in slope-intercept form.

2. Graph the y-intercept and slope.

3. Draw the line (solid or dashed). , Dashed line, Solid line

• Steps to Graphing Linear System Inequalities

, Above y-intercept

, Below y-intercept

4. Lightly shade above or below the y-intercept.

5. Graph the other equation. See #’s 3 and 46. Darkly shade overlap.

21

34

53

y x

y x

Ex.

Graph the system of linear inequalities.

2) Graph. Find m and b.3) Solid or dashed?

4) Lightly shade above or below the y-intercept?

1) Put in slope-intercept form.

5) Do the same for the other equation.6) Darkly shade overlap.

2

3m 1b

4

3m 5b

Solid Below

Dashed

Above

Class Notes: Systems of Inequalities

15

23 2

y x

y x

Graph the system of linear inequalities.

2) Find m and b, then graph

3) Solid or dashed?4) Lightly shade above or below the y-intercept?

1) Put in slope-intercept form.

5) Do the same for the other equation.

6) Darkly shade overlap.

1

2m 5b

3

1m 2b

Dashed Above

Dashed

Above

Write the system of inequalities that produced this graph.

Applying Systems of Equations (1)

Timmy has a pocket full of quarters and dimes. There are a total of 40 coins. When he added it up he counted $5.50. How many quarters does he have in his pocket?

Ex.

x =

y =

# of quarters

# of dimes

40x y .25 .10 5.50x y 100 100 100

25x 10y 55010x

40x y 40y 1010 10

30y

10 quarters

1. Mark the text.2. Label variables.

3. Create equations.

4. Solve.

10 10 10

10y 400

15 150x

10x 15 15

Let’s eliminate

the ‘Y’

Substitute into ANY original equation.

Notes

2 4

2 12

x y

x y

Ex.

Graph the system of linear inequalities.

2

1m 4b

1

2m 6bDashed

AboveSolid

Below

2 4x y 2 12x y 2 2x x

2 4y x x x 2 12y x 2 2 2

16

2y x

Notes

3 2 8

6 2 10

x y

x y

Ex.

Graph the system of linear inequalities.

3

2m 4b

3

1m 5b

Solid

Below

Dashed

Above

3 2 8x y 6 2 10x y 3 3x x 2 3 8y x 2 2 2

34

2y x

6 6x x 2 6 10y x 2 2 2

3 5y x

Class Work/Test Review:

See Handout

2 Make a Plan

Write a system of equations, one equation to represent the cost of Club A and one for Club B. Let x be the number of movies rented and y the total cost.

Totalcost is price

for eachrental plus

member-ship fee.

Club A y = 3 x + 10

Club B y = 2 x + 15

Check It Out! Example 3 Continued