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# February 7, 2014

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• 1. Warm Up: (3) 2. What is the solution to the following system of equations: 2(m + n) + m = 9 3m - 3n = 24
• 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. 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. 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. 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. Write the system of inequalities that produced this graph.
• 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. 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. 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. Class Work/Test Review: See Handout
• 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