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Do Now 1/20/10

Do Now 1/20/10. Take out HW from last night. Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36 Copy HW in your planner. Benchmark Test #1 evens Text p. 469, #3-8 all, #10-38 evens Quiz sections 7.5 – 7.6 Friday. 1) inconsistent 2) consistent dependent

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Do Now 1/20/10

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  1. Do Now 1/20/10 • Take out HW from last night. • Text p. 462, #1-8 all, #10, #12, #16-30 evens, #36 • Copy HW in your planner. • Benchmark Test #1 evens • Text p. 469, #3-8 all, #10-38 evens • Quiz sections 7.5 – 7.6 Friday

  2. 1) inconsistent 2) consistent dependent 3) lines have same slope but different y-intercepts 4) the graph would show only one line 5) B; one solution 6) C; no solution 7) A; infinitely many solutions 8) no solution 10) one solution 12) infinitely many solutions 16) infinitely many solutions 18) infinitely many solutions 20) no solution 22) (3,0) 24) C 26) no solution 28) one solution 30) one solution 36) No, there are infinitely many solutions Homework Text p. 462, #1-8 all, #10, #12, #16-30 evens & 36

  3. Objective • SWBAT solve systems of linear inequalities in two variables

  4. Section 6.7 “Graph Linear Inequalities” Remember This??? Linear Inequalities- the result of replacing the = sign in a linear equation with an inequality sign. 2x + 3y > 4 y ≥ 4x - 3 y ≤ ½x + 3 7y < 8x - 16

  5. Remember This??? Graphing Linear Inequalities • Graphing Boundary Lines: • Use a dashed line for < or >. • Use a solid line for ≤ or ≥.

  6. Graph an Inequality Remember This??? Graph the inequality y > 4x - 3. STEP2 STEP3 STEP1 Graph the equation Test (0,0) in the original inequality. Shade the half-plane that contains the point (0,0), because (0,0) is a solution to the inequality.

  7. Graph an Inequality Remember This??? Graph the inequality x + 3y ≥ -1. STEP2 STEP3 STEP1 Shade the half-plane that contains the point (1,0), because (1,0) is a solution to the inequality. Graph the equation Test (1,0) in the original inequality.

  8. Graph an Inequality Remember This??? Graph the inequality y ≥ -3. STEP2 STEP3 STEP1 Shade the half-plane that contains the point (2,0), because (2,0) is a solution to the inequality. Graph the equation Test (2,0) in the original inequality. Use only the y-coordinate, because the inequality does not have a x-variable.

  9. Graph an Inequality Remember This??? Graph the inequality x≤ -1. STEP2 STEP3 STEP1 Shade the half-plane that does not contain the point (3,0), because (3,0) is not a solution to the inequality. Graph the equation Test (3,0) in the original inequality. Use only the y-coordinate, because the inequality does not have a x-variable.

  10. Section 7.6 “Solve Systems of Linear Inequalities” SYSTEM OF INEQUALITIES- consists of two or more linear inequalities in the same variables. x – y > 7 Inequality 1 2x + y < 8 Inequality 2 A solution to a system of inequalities is an ordered pair (a point) that is a solution to both linear inequalities.

  11. ? ? 1 > 0 – 2 1 > 0 + 6 1 > – 2 1 > 6 Graph a System of Inequalities y > -x – 2 Inequality 1 y ≤ 3x + 6 Inequality 2 Graph both inequalities in the same coordinate plane. The graph of the system is the intersection of the two half-planes, which is shown as the darker shade of blue. (0,1)

  12. ? ? 0 < 5 – 4 0≥-5 + 3 0 < 1 0≥ -2 Graph a System of Inequalities y < x – 4 Inequality 1 y ≥ -x + 3 Inequality 2 Graph both inequalities in the same coordinate plane. The graph of the system is the intersection of the two half-planes, which is shown as the darker shade of blue. (5,0)

  13. ? ? ? x + 2y ≤ 4 y ≥ -1 x > -2 0≥ -1 0 + 0 ≤ 4 0 > -2 Graph a System of THREE Inequalities y ≥ -1 Inequality 1: Graph all three inequalities in the same coordinate plane. The graph of the system is the triangular region, which is shown as the darker shade of blue. x > -2 Inequality 2: x + 2y ≤ 4 Inequality 3: Check (0,0)

  14. Graph a System of THREE Inequalities y ≥ -x + 2 y > -x Inequality 1: Inequality 1: y < 4 y ≥ x – 4 Inequality 2: Inequality 2: x < 3 y < 5 Inequality 3: Inequality 3:

  15. Write a system of inequalities for the shaded region. y > 2x + 1 y ≥ 3 Inequality 1 INEQUALITY 1: One boundary line for the shaded region is y = 3. Because the shaded region is above the solid line, the inequality is y ≥ 3. Inequality 2 Write a System of Linear Inequalities INEQUALITY 2: Another boundary line for the shaded region has a slope of 2 and a y-intercept of 1. So, its equation is y = 2x + 1. Because the shaded region is above the dashed line, the inequality is y > 2x + 1.

  16. Homework NJASK7 Prep • Text p. 469, #3-8 all, #10-38 evens

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