7.6 Graphing Systems of Linear Inequalities Algebra 7.6 Graphing Systems of Linear Inequalities

REVIEW: Graph of Linear Inequality Looks like this (shaded half-plane) The solutions are all the points in the shaded region

Graph of System of Linear Inequalities Looks like this (shaded region between two lines) The solutions are all the points in the shaded region

Shade the overlap To shade above both lines

Shade the overlap To shade above one line and below the other

Shade the overlap To shade above one line and below the other

Shade the overlap To shade below both lines

Steps to Graphing Graph the lines for each linear inequality in the same plane. Locate half-plane to shade for each line (above or below). The region that is overlapping (in both solution areas) is the one to shade.

Example Graph the system: y < 3 y > 1 The solution region is below the line y = 3 and above the line y = 1.

Example Graph the system: y < ½ x + 1 y > ½ x - 2 The solution region is below the line y = ½ x + 1 and above the line y = ½ x - 2

Example Graph the system: y < -½ x + 1 y ≥ ½ x - 1 The solution region is above the line y = ½ x - 1 and below the line y = -½ x + 1

Example Graph the system: y > -x - 1 y ≥ 2x - 8 The solution region is above the line y = 2x - 8 and above the line y = -x - 1

Example Graph the system: x > -3 y < 1 y > x - 2 VERTICAL HORIZONTAL The solution region is right of the line x = -3 below the line y = 1 and above the line y = x - 2

Homework pg. 435 # 9-22