 # 8.8 Linear Inequalities, Systems, and Linear Programming.

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8.8 Linear Inequalities, Systems, and Linear Programming

Linear Inequalities in Two Variables An inequality that can be written as Ax + By < C where A, B, and C are real numbers (A or B cannot both be 0), is a linear inequality in two variables. – The, ≤, or ≥. The graphs of linear inequalities in two variables are regions and may include a boundary line. – For the above example, the boundary line would be the graph of the equation Ax + By = C.

Graphing a Linear Inequality Graph 3x + 2y ≥ 6. 1.Draw the boundary. – Graph the equation. – Solid or dotted? 2.Shade the appropriate region. – Above or below? – Test point

 Graph x – 3y > 4.

Systems of Inequalities Graphing a system of inequalities is similar to graphing a system of equations. 1.Graph each inequality (using the method we applied to the previous examples) in the same coordinate system. 2.Find the intersection of the regions of solutions.

Graphing a System of Inequalities Graph the solution set of the linear system. 3x + 2y ≤ 6 2x – 5y ≥ 10

 Graph the solution set of the linear system. 2x + 3y ≥ 12 7x + 4y ≥ 28 y ≤ 6 x ≤ 5