1.4 and 1.5 Graph Linear Inequalities in Two Variables/Systems of Linear Inequalities Inequalities Test: 2/26/10

Vocabulary A linear inequality in two variables can be written in one of four forms: 1. Ax + By < C 2. Ax + By < C 3. Ax + By > C 4. Ax + By > C

Vocabulary An ordered pair (x, y) is a solution of a linear inequality in two variables if the inequality is true when the values of x and y are substituted into the inequality. The graph of a linear inequality in two variables is the set of all points in a coordinate plane that represent solutions of the inequality. A line divides the plane into two half-planes.

Example 1: Tell whether the ordered pairs (5, -1) and (-2, 6) are solutions of the inequality 2x + 3y > 9.

You Try: Tell whether the given ordered pairs are solutions of the inequality. 1. 4x – y < 2; (2, 4) and (1, -3) 2. 3/2x + 5y > 15; (-2, 4) and (0, -3)

Example 2: Graph y > 1 in a coordinate plane.  Would your line be a solid or dashed line? Why?  For the inequality > where would you shade? Why?  Identify a solution.

Example 2 Cont’d: Graph 2x + y < -3  Would your line be a solid or dashed line? Why?  For the inequality < where would you shade? Why?  Identify a solution.

You Try: Graph the inequality in a coordinate plane. 1. x < y < 3x 3. x – 4y < 8

Example 3: The perimeter of a rectangle is to be more than 16 inches. Write an inequality describing the possible dimensions of the rectangle. Then graph the inequality and identify three solutions.  Step 1: Write an inequality for the perimeter of the rectangle.  Step 2: Graph the inequality  Step 3: Identify three solutions.

Example 3 Cont’d: Inequality: 2x + 2y > 16 Three Solutions:

Example 4: Graph y < |x| + 1  Would your line be a solid or dashed line? Why?  For the inequality < where would you shade? Why?  Identify a solution.

You Try: Graph the inequality  Think about your transformations to help you graph. 1. y < 3|x| 2. y > -|x| y > |x + 2| - 1

Vocabulary The following is an example of a system of linear inequalities in two variables:  x + y 6 A solution of a system of inequalities is an ordered pair that is a solution of each inequality in the system. The graph of a system of inequalities is the graph of all solutions of the system.  We call this the feasible region.

Try These Systems: Graph each system, and identify a solution. 1. y - 2x 2. y > x + 2, y < x y > 0, y < |x – 1|

Try These Answers:

Try a System of 3! Graph the system of inequalities and identify a solution. 1. y < -x + 2 x > 1 y > -2