Warm Up: (3)

2. What is the solution to the following system of equations:
2(m + n) + m = 9
3m - 3n = 24
Warm Up: A Note about Solving by Elimination

4) Substitute into ANY
original equation.

2x + 3y = 12
-2 = 5y – 4x
2

2

2...
Class Notes: Systems of Inequalities(3)
• Steps to Graphing Linear System Inequalities
1. Write the equation in slope-inte...
Class Notes: Systems of Inequalities
Graph the system of linear inequalities.
Ex.
2
2
b
1 Solid
y
x 1 m

3

3

y

m

4
x 5...
Graph the system of linear inequalities.
1) Put in slopeintercept form.

y
y
m

1
m
x 5
2
3x 2
3
b
1

Dashed
Above

2

1
2...
Write the system of inequalities that produced this graph.
Applying Systems of Equations (1)
Ex. Timmy has a pocket full of quarters and dimes. There are a
total of 40 coins. When h...
Notes
Graph the system of linear inequalities.
Ex.

2x y

4

x 2 y 12
2x y
2x
y

m

x 2 y 12
x
x

4
2x
2x 4

2
b
1
Dashed
...
Notes
Graph the system of linear inequalities.
Ex.

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

6 x 2 y 10
6x
6x

2y
2

2y
6 x 10
...
Class Work/Test Review:
See Handout
Check It Out! Example 3 Continued
2

Make a Plan

Write a system of equations, one equation to
represent the cost of Club ...
February 7, 2014
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February 7, 2014

  1. 1. Warm Up: (3) 2. What is the solution to the following system of equations: 2(m + n) + m = 9 3m - 3n = 24
  2. 2. Warm Up: A Note about Solving by Elimination 4) Substitute into ANY original equation. 2x + 3y = 12 -2 = 5y – 4x 2 2 2) Make opposites. 2 2 x 3 y 12 4x 5 y 2 x 3 y 12 2 2x 3 2 12 2x 6 12 6 6 2x 6 4x 6y 24 4x 5 y 2 11y 22 11 y 2 11 2 1) Arrange the variables. 3, 2 2 x 3 3) Add and solve for the variable. 5) Check your answer.
  3. 3. Class Notes: Systems of Inequalities(3) • Steps to Graphing Linear System Inequalities 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 4. Lightly shade above or below the y-intercept. , Above y-intercept , Below y-intercept 5. Graph the other equation. See #’s 3 and 4 6. Darkly shade overlap.
  4. 4. Class Notes: Systems of Inequalities Graph the system of linear inequalities. Ex. 2 2 b 1 Solid y x 1 m 3 3 y m 4 x 5 3 4 b 5 3 Dashed Above Below 1) Put in slope-intercept form. 2) Graph. Find m and b. 3) Solid or dashed? 4) Lightly shade above or below the y-intercept? 5) Do the same for the other equation. 6) Darkly shade overlap.
  5. 5. Graph the system of linear inequalities. 1) Put in slopeintercept form. y y m 1 m x 5 2 3x 2 3 b 1 Dashed Above 2 1 2 b 5 Dashed Above 2) Find m and b, then graph 3) Solid or dashed? 4) Lightly shade above or below the y-intercept? 5) Do the same for the other equation. 6) Darkly shade overlap.
  6. 6. Write the system of inequalities that produced this graph.
  7. 7. Applying Systems of Equations (1) Ex. 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? 10 x = # of quarters 10 x y 40 .25x .10 y 5.50 100 y = # of dimes 10 100 15x 150 Substitute into ANY original equation. 15 1. Mark the text. 2. Label variables. 100 25x 10 y 550 10x 10 y 400 15 Let’s eliminate the ‘Y’ x y 40 10 y 40 10 10 y 30 x 10 10 quarters 3. Create equations. 4. Solve.
  8. 8. Notes Graph the system of linear inequalities. Ex. 2x y 4 x 2 y 12 2x y 2x y m x 2 y 12 x x 4 2x 2x 4 2 b 1 Dashed Above 2y 2 4 y m x 12 2 2 1 x 6 2 1 b 6 2 Solid Below
  9. 9. Notes Graph the system of linear inequalities. Ex. 3x 2 y 8 6 x 2 y 10 3x 2 y 8 3x 3x 6 x 2 y 10 6x 6x 2y 2 2y 6 x 10 2 2 2 y 3x 5 y m 3x 8 2 2 3 x 4 2 3 b 2 4 m 3 b 1 Solid Dashed Below Above 5
  10. 10. Class Work/Test Review: See Handout
  11. 11. Check It Out! Example 3 Continued 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. Total cost is price for each rental plus membership fee. Club A y = 3 x + 10 Club B y = 2 x + 15

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