3.3 graph systems of linear inequalities
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This document discusses how to solve systems of linear inequalities by graphing them. It explains that you first put the inequalities into slope-intercept form, then graph each line as dotted or solid based on the inequality symbols and shade the correct region above or below the line. The solution to the system is the region where the graphs overlap. An example demonstrates these steps to find the solution region between two inequalities.
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3.3 graph systems of linear inequalities
- 1. SYSTEMS OF LINEAR INEQUALITIES Solving Linear Systems of Inequalities by Graphing
- 2. Solving Systems of Linear Inequalities We show the solution to a system of linear inequalities by graphing them. a) This process is easier if we put the inequalities into Slope-Intercept Form, y = mx + b. 1.
- 3. Solving Systems of Linear Inequalities 2. Graph the line using the y-intercept & slope. a) If the inequality is < or >, make the lines dotted. b) If the inequality is < or >, make the lines solid.
- 4. Solving Systems of Linear Inequalities 3. The solution also includes points not on the line, so you need to shade the region of the graph: above the line for ‘y >’ or ‘y ≥’. b) below the line for ‘y <’ or ‘y ≤’. a)
- 5. Solving Systems of Linear Inequalities Example: a: b: 3x + 4y > - 4 x + 2y < 2 Put in Slope-Intercept Form: a) 3x + 4 y > −4 4 y > − 3x − 4 3 y > − x −1 4 b) x + 2 y < 2 2 y < −x + 2 1 y < − x +1 2
- 6. Solving Systems of Linear Inequalities Example, continued: 3 a : y > − x −1 4 1 b : y < − x +1 2 Graph each line, make dotted or solid and shade the correct area. a: dotted shade above b: dotted shade below
- 7. Solving Systems of Linear Inequalities a: 3x + 4y > - 4 3 a : y > − x −1 4
- 8. Solving Systems of Linear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2 3 a : y > − x −1 4 1 b : y < − x +1 2
- 9. Solving Systems of Linear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2 The area between the green arrows is the region of overlap and thus the solution.
- 10. Solving Systems of Linear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2 The area between the green arrows is the region of overlap and thus the solution.