Algebra Tutorials!

 Tuesday 23rd of January

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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Graphing Inequalities in Two Variables

Objective Learn how to graph the solution sets of inequalities in two variables.

It is important that you understand that solving an inequality in two variables means describing the solution set for the inequality, and that graphing it means specifying a whole region, rather than a line or a curve. The solution procedure is similar to that for linear equations, involving the Addition and Multiplication Properties of Inequalities. That too should be clear before starting to read this lesson, since it connects these new ideas with ideas that are already familiar to you.

## Linear Inequalities

A linear inequality is an expression similar to a linear equation, except that it has an inequality symbol rather than an equals sign.

 Linear Inequalities Not Linear Inequalities 2x + 3y leq 7 + 5x x 2 + 5 geq y x + 5 geq 2y - 5 xy > 7 y < 5 y = x - 4

## Solution Sets to Linear Inequalities

Let's begin with an inequality in two variables, say 3y + 5 2x - 1. Then the solution set for the inequality is the collection of all ordered pairs (x , y) for which the inequality holds true. For example, the ordered pair (7, 0) is in the solution set because substituting 7 for x and 0 for y makes the inequality true.

 3(0) + 5 2(7) - 1 Replace (x, y) with (7, 0). 5 13

5 13 is a valid inequality.

On the other hand, the ordered pair (2, 4) is not in the solution set because substituting 2 and 4 for x and y , respectively, makes the inequality false.

 3(4) + 5 2(2) - 1 Replace (x, y) with (2, 4). 17 3

17 3 is not a valid inequality.