Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
3-3 Solving Systems of Inequalities by Graphing SWBAT: • Solve Systems if Inequalities by Graphing Recall: What is a Linear Inequality in Two Variables? A Linear Inequality is very similar in form to Linear Equations. } Where a solution to a Linear Equation is a coordinate, so is a solution to a Linear Inequality } } Linear Equations } } } } 2x + 3y = 6 y = 1/2 x – 3 y=4 Linear Inequalities } } } 2x + 3y < 6 y > 1/2 x – 3 y≥4 Check Solutions of 2x – 3y ≥ - 2. 1. 2. (0 , 0) 2x – 3y ≥ - 2 2(0) – 3(0) ≥ - 2 0 ≥-2 SOLUTION! (0 , 1) 2x – 3y ≥ - 2 2(0) – 3(1) ≥ - 2 -3 ≥ - 2 NO SOLUTION! 3. 4. (0 , -1) 2x – 3y ≥ - 2 2(0) – 3(-1) ≥ - 2 3 ≥-2 SOLUTION! (2 , -1) 2x – 3y ≥ - 2 2(2) – 3(-1) ≥ - 2 7 ≥-2 SOLUTION! Lets look at a graph of 2x – 3y ≥ - 2 } Notice how the solutions of our inequality are underneath the line… } The one non-solution is above our graphed line… Lets look at a graph of 2x – 3y ≥ - 2 Any Coordinate that is in that Blue Shaded area would be a Solution to the Inequality. } What do you think about any coordinate in the white section? } What about on the line? } Graphing a Linear Inequalities… Step 1: Write the Inequality in Slope Intercept form. Graph the Inequality. Use a Dashed Line for < or > and a Solid Line for ≥ or ≤. Step 2: Test the Coordinates of a point in one of the sections of the Graph. Step 3: Shade the half of the graph where the coordinate is if it is a solution to the inequality. If it is not a solution shade the other side of the graph. Use Slope Intercept Form } Graph the inequality x + y > 3 } } } Pick a coordinate. } } First Write in Slope Intercept Form (minus x from both sides) y > -x +3 (graph the equation y = -x + 3) Pick any value not on the line. See if it is a solution. } } Shade the side the coordinate is on if it is a solution to the inequality, Shade the other side if it doesn’t. Use Slope Intercept Form } Graph the inequality 2x – y ≥ -2 } } } Pick a coordinate. } } First Write in SI Form (minus 2x from both sides, divide by -1) y ≤ 2x +2 (Graph the equation y = 2x + 2) Pick any value not on the line. See if it is a solution. } } Shade the side the coordinate is on if it is a solution to the inequality, Shade the other side if it doesn’t. Graph a Vertical Line } Graph the inequality x < -2 } } Pick a coordinate. } } Think about the equation x = -2 Pick any value not on the line. See if it is a solution. } } Shade the side the coordinate is on if it is a solution to the inequality, Shade the other side if it doesn’t. Graph a Horizontal Line } Graph the inequality y ≤ 1 } } Pick a coordinate. } } Think about the equation y = 1 Pick any value not on the line. See if it is a solution. } } Shade the side the coordinate is on if it is a solution to the inequality, Shade the other side if it doesn’t. Graphing Systems of Linear To Solve a System of Inequalities, we need to find the ordered pairs that satisfy all the inequalities in the system. } One way to solve a system is to graph the inequalities on the coordinate plane. } The solution will be the intersection of the graphs or where they overlap. } Ex 1: Graph a System of Inequalities Ex 1B: Graph a System of Inequalities Ex 1C: Graph a System of Inequalities Ex 2: Separate Regions Ex 3: More Inequalities! x ≤1 y < 2x +1 x + 2y ≥ −4