Objective solve systems of linear inequalities in two variables

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

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

Graph the inequality y > 4x - 3. Graph an Inequality Remember This??? Graph the inequality y > 4x - 3. STEP 2 STEP 3 STEP 1 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.

Graph the inequality x + 3y ≥ -1. Graph an Inequality Remember This??? Graph the inequality x + 3y ≥ -1. STEP 2 STEP 3 STEP 1 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.

Graph the inequality y ≥ -3. Graph an Inequality Remember This??? Graph the inequality y ≥ -3. STEP 2 STEP 3 STEP 1 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.

Graph the inequality x ≤ -1. Graph an Inequality Remember This??? Graph the inequality x ≤ -1. STEP 2 STEP 3 STEP 1 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.

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.

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 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) 1 > 0 – 2 ? 1 ≤ 0 + 6 ? 1 > – 2 1 ≤ 6

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) 0 < 5 – 4 ? 0 ≥ -5 + 3 ? 0 < 1 0 ≥ -2

Graph a System of THREE Inequalities 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: x + 2y ≤ 4 ? y ≥ -1 ? x > -2 ? Check (0,0) 0 ≥ -1 0 > -2 0 + 0 ≤ 4

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:

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