9.5 Inequalities in Two Variables

1. 9.5 Inequalities in Two Variables Ca 6.0 Sketch the region defined by linear inequalities

2. Is this ordered pair a solution? Example 1: Is (5, -3) a solution to 2x – y > 5? Substitute… 2(5) – (-3) > 5 10 + 3 >5 13 > 5 This is a true statement so, yes, (5, -3) is a solution.

3. Try this… 1.) Is (2, 1) a solution to x + y < 4? 2 + 1 < 4 3 < 4 Yes, it is a solution 2.) Is (4,8) a solution to y > 2x + 1? 8 > 2(4) + 1 8 > 8 + 1 8 > 9 No, it is not a solution

4. x + y < 4 1.) Graph the line. (Using intercepts, two points, or slope intercept form) Using intercepts X intercept x + 0 < 4 x < 4 (4,0) Y intercept 0 + y < 4 y < 4 (0,4) Graphing Inequalities in Two Variables

5. 2.) Solid or dashed? < or > dashed < or > solid x + y < 4

6. 3.) Shading? Choose any point on the coordinate plane. If it is a solution to the inequality you shade the region where that point is, if not, then shade the opposite region. I choose (0, 0) 0 + 0 < 4 0 < 4,true, so I will shade below the line x + y < 4

7. Graph y – 2x > 0 Using slope intercept. y – 2x > 0 + 2x + 2x y > 2x y intercept is (0, 0) Slope is 2

8. 2.) Solid line because of the > 3.) I am going to try the point (2,0) 0 > 2(2) 0 > 4 No, so shade above the line y > 2x

9. Try this… Graph y > x – 1