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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 Homework Text p. 462, #1-8 all, #10, #12, #16-30 evens & 36 1) inconsistent 12) infinitely many solutions 2) consistent dependent 3) lines have same slope 16) infinitely many solutions but different y-intercepts 4) the graph would show 18) infinitely many solutions only one line 20) no solution 5) B; one solution 22) (3,0) 6) C; no solution 24) C 7) A; infinitely many solutions 26) no solution 8) no solution 28) one solution 10) one solution 30) one solution 36) No, there are infinitely many solutions Objective SWBAT solve systems of linear inequalities in two variables Section 6.7 “Graph Linear Inequalities” Linear Inequalitiesthe result of replacing the = sign in a linear equation with an inequality sign. 2x + 3y > 4 y ≤ ½x + 3 y ≥ 4x - 3 7y < 8x - 16 Graphing Linear Inequalities Graphing Boundary Lines: Use a dashed line for < or >. Use a solid line for ≤ or ≥. Graph an Inequality Graph the inequality STEP 1 Graph the equation y 4x 3 STEP 2 Test (0,0) in the original inequality. y 4x 3 0 4(0) 3 True y > 4x - 3. STEP 3 Shade the half-plane that contains the point (0,0), because (0,0) is a solution to the inequality. Graph an Inequality Graph the inequality STEP 1 Graph the equation x 3 y 1 STEP 2 Test (1,0) in the original inequality. x 3 y 1 1 3(0) 1 True x + 3y ≥ -1. STEP 3 Shade the half-plane that contains the point (1,0), because (1,0) is a solution to the inequality. Graph an Inequality Graph the inequality STEP 1 Graph the equation y 3 STEP 2 Test (2,0) in the original inequality. Use only the ycoordinate, because the inequality does not have a x-variable. y 3 (0) 3 True y ≥ -3. STEP 3 Shade the half-plane that contains the point (2,0), because (2,0) is a solution to the inequality. Graph an Inequality Graph the inequality STEP 1 Graph the equation x 1 STEP 2 Test (3,0) in the original inequality. Use only the ycoordinate, because the inequality does not have a x-variable. x 1 ( 0 ) 1 False x ≤ -1. STEP 3 Shade the half-plane that does not contain the point (3,0), because (3,0) is not a solution to the inequality. Section 7.6 “Solve Systems of Linear Inequalities” SYSTEM OF INEQUALITIESconsists 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. Solving a System of Inequalities by Graphing (1) Graph both inequalities in the same plane. (2) Find the intersection of the two half-planes. The graph of the system is this intersection. (3) Check a coordinate by substituting into EACH inequality of the system, to see if the point is a solution for both inequalities. Graph a System of Inequalities Inequality 1 y > -x – 2 Inequality 2 y ≤ 3x + 6 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) ? 1>0–2 1>–2 ? 1>0+6 1>6 Graph a System of Inequalities Inequality 1 y<x–4 Inequality 2 y ≥ -x + 3 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) ? 0<5–4 0< 1 ? 0 ≥ -5 + 3 0 ≥ -2 Graph a System of THREE Inequalities Inequality 1: Inequality 2: Inequality 3: Check (0,0) y ≥ -1 x > -2 x + 2y ≤ 4 ? y ≥ -1 0 ≥ -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 0 > -2 ? x + 2y ≤ 4 0+0≤4 Graph a System of THREE Inequalities Inequality 1: Inequality 2: Inequality 3: y ≥ -x + 2 y<4 x<3 Inequality 1: Inequality 2: Inequality 3: y > -x y≥x–4 y<5 Write a System of Linear Inequalities Write a system of inequalities for the shaded region. 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: 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. y≥3 y > 2x + 1 Inequality 1 Inequality 2 NJASK7 Prep Homework Text p. 469, #3-8 all, #10-38 evens