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3.3 SYSTEMS OF LINEAR INEQUALITIES

3.3 SYSTEMS OF LINEAR INEQUALITIES. Solving Linear Systems of Inequalities by Graphing. Objective. You will graph systems of linear inequalities. Solving Systems of Linear Inequalities. We show the solution to a system of linear inequalities by graphing them.

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3.3 SYSTEMS OF LINEAR INEQUALITIES

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  1. 3.3 SYSTEMS OF LINEAR INEQUALITIES Solving Linear Systems of Inequalities by Graphing

  2. Objective • You will graph systems of linear inequalities.

  3. 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.

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

  5. 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 ≤’

  6. Solving Systems of Linear Inequalities Example: Eq ‘a’: 3x + 4y > - 4 Eq ‘b’: x + 2y < 2 Put each Equation in Slope-Intercept Form. ‘a’: ‘b’:

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

  8. Solving Systems of Linear Inequalities Eqn ‘a’: 3x + 4y > - 4

  9. Solving Systems of Linear Inequalities Eqn ‘a’: 3x + 4y > - 4 Eqn ‘b’: x + 2y < 2

  10. Solving Systems of Linear Inequalities The place where the two shadings overlap is your solution region. The area between the green arrows is the region of overlap.

  11. Graph a system with an absolute value inequality • Graph the system of inequalities. y ≥ 0 y < |x – 1|

  12. Graph each inequality in the system. • Identify the region that is common to both graphs. It is the region that is shaded darkest.

  13. Graph a system of three or more inequalities y ≤ -x + 2 x ≥ 1 y > -2 • Graph each inequality and identify the region that is shaded darkest.

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