Systems of Inequalities Lecture

Introduction

• Focus on systems of inequalities
• Similar to previous lessons, it's an extension of prior knowledge
• Will incorporate this topic with the rest of the lesson

Graphing Systems of Inequalities

• Example with two inequalities
  • Objective: Graph the solution where they intersect

Step-by-Step Process

1. Convert to Slope-Intercept Form

   • Example given: x + y < 4
   • Convert to: y < -x + 4
     • Subtract x from both sides
   • Remember:
     • Negative slopes: Consider as fractions (e.g., -1 as -1/1)
     • Use fractions for slope calculations

2. Plotting the Graph

   • Y-Intercept: Plot the constant term first
     • Example: Go up to +4 on y-axis
   • Slope: Use change in y over change in x
     • Example: Down 1 (negative change in y), right 1 (positive change in x)

3. Drawing the Line

   • Check inequality symbol
   • If < or >, use dashed line
   • Use shading to determine solution area
     • Test point: (0,0) to check inequality
     • If true, shade below the line

4. Graph the Second Inequality

   • Example already in slope-intercept form
   • Slope: 1/1
   • Y-Intercept: -3
     • Go down 3 on y-axis
   • Slope: Up 1, right 1
   • If ≥ or ≤, use a solid line
   • Test point and shading
     • Test point: Check (0,0) against inequality
     • If true, shade above the line

5. Identify Solution Region

   • Region where both inequalities are true
   • Graph visually shows intersection area

Conclusion

• Systems of inequalities involve graphing two inequalities on the same plane
• Look for regions where both conditions are satisfied

Note: Use arrows for shading to simplify graph and avoid clutter.