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Linear Inequalities in Two Variables: Examples and Solutions

Learn about linear inequalities in two variables, how to solve them, and how to graph the solution sets using examples and a step-by-step process.

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Linear Inequalities in Two Variables: Examples and Solutions

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  1. Chapter 4 Section 4 Linear Inequalities in Two Variables

  2. Linear Inequality in Two Variables • Ax + By = C • Straight lines when graphed. • Replace the = symbol with an inequality • Linear Inequality in Two Variables

  3. Examples • x + y > 2 • 5y ≤ 15 • 2x – y > 4

  4. Solution of an inequality • Two variables • Ordered pair of real number that satisfy the inequality • Graph • Region, half plane • Solid line: line is part of the graph • Dashed line: not part of the graph

  5. Solve • Replace the inequality symbol with = • Graph the line • Choose a test point. • True statement, shade that part of the half plane that contains the test point.

  6. Practice • Solve and graph the solution set • 2x – 3y < 6

  7. Graph the solution set • 2x + y > 6 • x ≤ - 4

  8. System of Linear Inequalities • Two or more linear inequalities • Solution • Ordered pair that satisfies each inequality in the system

  9. Graph the solution • Solution • Replace the inequality with = • Graph each line • Lines intersect, so pick a test point in each region.

  10. One more • Graph the solution set

  11. Graph the Solution set c) d)

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