Linear Inequalities in 2 Variables 3.3 Linear Inequalities in 2 Variables

OBJECTIVES: Solve and Graph a linear inequality in 2 variables. Use a linear inequality in 2 variables to solve real-world problems.

Definition: Linear Inequality in 2 Variables Using variables x & y, it is any inequality that can be written in one of the forms below, where A ≠ 0 and B ≠ 0. Ax + By ≥ C Ax + By > C Ax + By ≤ C Ax + By < C

SOLUTION… Ordered Pair  (x, y) A region of the coordinate plane & is called a half-plane bounded by a boundary line.

Graph: y < x + 2 Graph the line. Use a dashed line because the values on this line are not included in the solution Choose a point such as (0, 0) to test. Since (0, 0) satisfies the inequality, shade the region that contains the point

Graph: y ≥ -2x + 3 Graph the boundary line. Use a solid line because the values on this line are included in the solution Choose a point like (0, 0) to test Since (0, 0) does not satisfy the inequality, shade the region that does not contain this point.

Extra Examples, If Needed… y > -2x – 2 y ≤ 2x + 5

GRAPH: -2x – 3y ≤ 3 Sometimes, you may need to solve for for y before graphing.

Graph: 3x – 4y ≥ 4

SOLUTION to 1 variable equations A half-plane Graph: x > -2

Example Graph: y ≤ -1

ACTIVITY PG. 175