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Further preview of Sec 5.2.1

Further preview of Sec 5.2.1. Objective: solve a system of two linear inequalities in two variables and to Graph the solution sets. Warm Up. 1. Determine whether the point P is a solution of the linear inequality 2. Solve the linear system (use any method). 3x + 4y = 5 -2x + y = 4.

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Further preview of Sec 5.2.1

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  1. Further preview of Sec 5.2.1 Objective: solve a system of two linear inequalities in two variables and to Graph the solution sets.

  2. Warm Up 1. Determine whether the point P is a solution of the linear inequality 2. Solve the linear system (use any method). 3x + 4y = 5 -2x + y = 4

  3. Quick Review = • What is the difference between an equation and an inequality? Which one is shaded? • When is the line solid? • When is the line dashed (dotted)? • How do you figure out where to shade? Graph this inequality: y > x – 2 m = 1 b = -2 <,> Inequality ≤, ≥ <, > Pick a point to plug in.

  4. Check if it’s a solution 1. (4, 10) 9x – y ≥ 23 5x + 0.2y ≥ 20 2. (2, -1) y ≤ 4x + 1 y > -x + 2 5(4) + 0.2(10) ≥ 20 20 + 2 ≥ 20 22 ≥ 20  9(4) – 10 ≥ 23 36 – 10 ≥ 23 26 ≥ 23  YES -1 ≤ 4(2) + 1 -1 ≤ 8 + 1 -1 ≤ 9  -1 > -(2) + 2 -1 > 0  NO

  5. Graphing Systems of Linear Inequalities Graph each system 3. y < 2 4. y > x – 2 x ≥ -1y ≤ - ½ x + 3

  6. Graphing Systems of Linear Inequalities Graph each system 5. y > 2x – 5 6. y ≥ -x + 2 3x + 4y < 122x + 4y < 4

  7. Writing Systems of Linear Inequalities Equation Write the inequalities for each system 7. 8.

  8. Wrap Up Checking solutions – have to work for both equations Graphing Inequalities dashed (dotted) - < or > solid - ≤ or ≥ shading – pick a point Writing equations of inequalities HW: P. 320 #19-23 odd, 29-43 odd Write DLUQ for notes

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