1. Yes, (0, 0) is a solution because it lies within the shaded region representing the solution set of the system.
2. The correct ordered pair is d. (-3, -1), as it is the only point located within the shaded triangular region on the graph.
3. No, (-2, 4) is not a solution because it does not lie within the shaded region of the graph.
4. To solve y < 3x - 4 and y ≥ -2x + 1 by graphing:
- Graph the line y = 3x - 4 as a dashed line (since it's a strict inequality) and shade below it.
- Graph the line y = -2x + 1 as a solid line (since it includes equality) and shade above it.
- The solution is the overlapping shaded region where both conditions are met.
5. To solve 2x + y > -4 and x - 2y ≤ 4 by graphing:
- Graph the line 2x + y = -4 as a dashed line and shade above it.
- Graph the line x - 2y = 4 as a solid line and shade above it (test point (0,0): 0 - 0 ≤ 4 is true).
- The solution is the overlapping shaded region.
6. To solve y ≤ (2/3)x + 2 and y > -x - 3 by graphing:
- Graph the line y = (2/3)x + 2 as a solid line and shade below it.
- Graph the line y = -x - 3 as a dashed line and shade above it.
- The solution is the overlapping shaded region.
Parent Tip: Review the logic above to help your child master the concept of graphing systems of linear equations worksheet.
