Presentation on theme: "Linear Inequalities in 2 Variables"— Presentation transcript:
1 Linear Inequalities in 2 Variables 3.3Linear Inequalities in 2 Variables
2 OBJECTIVES: Solve and Graph a linear inequality in 2 variables. Use a linear inequality in 2 variables to solve real-world problems.
3 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 ≥ CAx + By > CAx + By ≤ CAx + By < C
4 SOLUTION… Ordered Pair (x, y) A region of the coordinate plane & is called a half-plane bounded by a boundary line.
5 Graph: y < x + 2 Graph the line. Use a dashed line because the values on this line are not included in the solutionChoose a point such as (0, 0) to test.Since (0, 0) satisfies the inequality, shade the region that contains the point
6 Graph: y ≥ -2x + 3 Graph the boundary line. Use a solid line because the values on this line are included in the solutionChoose a point like (0, 0) to testSince (0, 0) does not satisfy the inequality, shade the region that does not contain this point.
7 Extra Examples, If Needed… y > -2x – 2y ≤ 2x + 5
8 GRAPH: x – 3y ≤ 3Sometimes, you may need to solve for for y before graphing.