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SYSTEMS OF INEQUALITIES Mr. Velazquez Honors Precalculus

Transcript of Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace...

Page 1: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

SYSTEMS OF INEQUALITIES Mr. Velazquez

Honors Precalculus

Page 2: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

INEQUALITIES IN TWO VARIABLES

The solution of an inequality of two variables, 𝒙 and 𝒚, is an ordered pair of real numbers such that when substituted into the inequality, we obtain a true statement. Each ordered pair solution is said to satisfy the inequality.

Page 3: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

GRAPHING LINEAR INEQUALITIES

A half-plane is the set of all points on one side of a line.

A half plane is the graph of an inequality that involves

> or <. The graph of an inequality that involves or

is a half-plane and a line.

A solid line is used to show that

a line is part of a graph. A dashed line is used to show that

a line is not part of a graph.

Page 4: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

GRAPHING LINEAR INEQUALITIES

Page 5: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

GRAPHING LINEAR INEQUALITIES

Page 6: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

GRAPHING WITHOUT TEST POINTS

Page 7: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

GRAPHING NONLINEAR INEQUALITIES

Page 8: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

GRAPHING NONLINEAR INEQUALITIES

Page 9: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

SYSTEMS OF INEQUALITIES

To solve a system of inequalities, we must graph both inequalities and find the area where both shaded regions coincide. This region will contain all possible solutions for the system of inequalities.

Page 10: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

GRAPHING NONLINEAR INEQUALITIES

Page 11: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

GRAPHING NONLINEAR INEQUALITIES

Page 12: Systems of Inequalities - WordPress.com · Graphing a Linear Inequality in Two Variables 1. Replace the inequality symbol with an equal sign and graph the corresponding linear equation.

CLASSWORK & HOMEWORK

CLASSWORK: SYSTEMS OF INEQUALITIES

Solve the following system of inequalities by graphing the solution.

HOMEWORK:

Systems of Equations HW 3

(MathXL)


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