Algebra and Trigonometry, 5th Edition

9.7 Systems of Inequalities and Linear Programming

• Graph linear inequalities.

• Graph systems of linear inequalities.

• Solve linear programming problems.

A graph of an inequality is a drawing that represents its solutions. We have already seen that an inequality in one variable can be graphed on the number line. An inequality in two variables can be graphed on a coordinate plane.

SOLVE LINEAR INEQUALITIES

REVIEW SECTION 1.6

Graphs of Linear Inequalities

A statement like $5x-4y<20$ is a linear inequality in two variables.

Linear Inequality in Two Variables

A linear inequality in two variables is an inequality that can be written in the form

$$Ax+By<C,$$

where A, B, and C are real numbers and A and B are not both zero. The symbol $<$ may be replaced ...