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SYSTEMS OF LINEAR INEQUALITIES

SYSTEMS OF LINEAR INEQUALITIES. Solving Linear Systems of Inequalities by Graphing. Solving Systems of Linear Inequalities. We show the solution to a system of linear inequalities by graphing them.

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SYSTEMS OF LINEAR INEQUALITIES

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  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. • This process is easier if we put the inequalities into Slope-Intercept Form, y = mx + b.

  3. Solving Systems of Linear Inequalities • Graph the line using the y-intercept & slope. • If the inequality is < or >, make the lines dashed. • If the inequality is < or >, make the lines solid.

  4. Solving Systems of Linear Inequalities • 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 ’. • below the line for ‘y <’ or ‘y ≤’.

  5. Solving Systems of Linear Inequalities Example: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

  6. a: dotted shade above b: dotted shade below Solving Systems of Linear Inequalities Example, continued: Graph each line, make dashed or solid and shade the correct area.

  7. Solving Systems of Linear Inequalities a: 3x + 4y > - 4

  8. Solving Systems of Linear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2

  9. Solving Systems of Linear Inequalities The area between the green arrows is the region of overlap and thus the solution. a: 3x + 4y > - 4 b: x + 2y < 2

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