To sketch the solution for the system of inequalities:

y > -x-2

y <-5x + 2

To sketch the solution of the system of inequalities:

1. **Graph the lines** associated with the boundaries of the inequalities first. These lines are:

   - \( y = -x - 2 \) (associated with \( y > -x - 2 \))
   - \( y = -5x + 2 \) (associated with \( y < -5x + 2 \))

2. **Determine whether to shade above or below each line** based on the inequality:
   - For \( y > -x - 2 \), you shade **above** the line since the inequality is strict (\(>\)).
   - For \( y < -5x + 2 \), you shade **below** the line since the inequality is also strict (\(<\)).

3. **Plotting the lines**:
   - For \( y = -x - 2 \), the y-intercept is \( (0, -2) \) and the slope is -1 (down 1, right 1).
   - For \( y = -5x + 2 \), the y-intercept is \( (0, 2) \) and the slope is -5 (down 5, right 1).

4. **Dotted lines**: Since the inequalities are strict (i.e., no equal sign), use **dashed** lines for both.

5. **Intersection of the shaded regions**: The solution to the system is the region where both shaded areas overlap.

Would you like a detailed sketch of this system?

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Here are some follow-up questions for better understanding:

1. How do you determine where to shade in a system of inequalities?
2. What does it mean when the lines in inequalities are dashed?
3. How do you find the points of intersection of two linear inequalities?
4. How do different slopes affect the position of the lines in the plane?
5. Can you solve the system of inequalities algebraically without graphing?

**Tip:** Always pay attention to whether inequalities include or exclude the boundary lines. Use dashed lines for strict inequalities and solid lines for inclusive ones.

To sketch the solution for the system of inequalities: y > -x-2, y < -5x + 2

Explore how to graph the system of inequalities y > -x - 2 and y < -5x + 2. Learn how to find the slope, intercept, and shaded regions, and understand the significance of dashed lines for strict inequalities. This guide provides a step-by-step solution for students in Grades 9-10.

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