We are given the following system of inequalities:

1. \( y > -3x + 4 \)
2. \( y < x - 2 \)

Let's solve this system of inequalities by graphing each inequality.

1. **Inequality 1: \( y > -3x + 4 \)**
   - The boundary line is \( y = -3x + 4 \), which is a straight line with a slope of -3 and a y-intercept of 4. The inequality is strict, so the region above the line (not including the line itself) represents the solution.

2. **Inequality 2: \( y < x - 2 \)**
   - The boundary line is \( y = x - 2 \), which has a slope of 1 and a y-intercept of -2. Again, the inequality is strict, so the solution is the region below this line (not including the line).

### Solution:
The solution is the region where the two inequalities overlap. To find this region:

1. Sketch the line \( y = -3x + 4 \) and shade the area above it.
2. Sketch the line \( y = x - 2 \) and shade the area below it.
3. The overlapping shaded region represents the solution to the system.

Would you like a visual representation or more details on how to plot these inequalities?

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Here are 5 related questions:

1. How would the solution change if the inequalities were non-strict (i.e., \( y \geq -3x + 4 \) and \( y \leq x - 2 \))?
2. What are the coordinates of the point where the two boundary lines intersect?
3. How would you describe the solution set in terms of coordinates?
4. Can you solve similar inequalities involving quadratic functions?
5. How does graphing help in solving systems of inequalities compared to algebraic methods?

**Tip:** When graphing inequalities, always consider whether the line should be solid (for \( \geq \) or \( \leq \)) or dashed (for \( > \) or \( < \)) to reflect the strictness of the inequality.

Learn how to solve the system of inequalities y > -3x + 4 and y < x - 2 by graphing each inequality. This problem involves key algebraic concepts such as graphing lines in slope-intercept form and finding the overlapping solution region. Suitable for students in Grades 9-10.

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