6.6 Systems of Linear Inequalities Standard: SWBAT solve a system of two linear inequalities in two variables and to sketch the solution sets.

Mini Quiz 54 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

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.

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

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

Graphing Systems of Linear Inequalities Graph each system 5. y > 2x – 5 6. y ≥ -x + 2 3x + 4y < 12 2x + 4y < 4

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