`x + y ge 4, 2x - y lt 0 `

Explanation

To solve the system of inequalities given by \( x + y \geq 4 \) and \( 2x - y < 0 \), we will follow a step-by-step approach.

### Step 1: Analyze the first inequality \( x + y \geq 4 \)

1. Rearrange the inequality to express \( y \) in terms of \( x \):
\[ y \geq 4 - x \]

2. Identify the boundary line by setting the equation to equality:
\[ y = 4 - x \]
This line will be solid since the inequality is greater than or equal to.

3. Find the intercepts:
- When \( x = 0 \):
\[ y = 4 \quad \text{(Point: (0, 4))} \]
- When \( y = 0 \):
\[ 0 = 4 - x \implies x = 4 \quad \text{(Point: (4, 0))} \]

### Step 2: Analyze the second inequality \( 2x - y < 0 \)

1. Rearrange the inequality to express \( y \) in terms of \( x \):
\[ y > 2x \]

2. Identify the boundary line by setting the equation to equality:
\[ y = 2x \]
This line will be dashed since the inequality is strictly less than.

3. Find the intercepts:
- When \( x = 0 \):
\[ y = 0 \quad \text{(Point: (0, 0))} \]
- When \( y = 0 \):
\[ 0 = 2x \implies x = 0 \quad \text{(Point: (0, 0))} \]

### Step 3: Plot the lines on a graph

1. Draw the line \( y = 4 - x \) (solid line) passing through points (0, 4) and (4, 0).
2. Draw the line \( y = 2x \) (dashed line) passing through the origin (0, 0).

### Step 4: Determine the feasible region

1. For the inequality \( y \geq 4 - x \), shade the region above the line (including the line).
2. For the inequality \( y > 2x \), shade the region above the dashed line (not including the line).

### Step 5: Identify the common region

1. The solution to the system of inequalities is the area where the shaded regions overlap.
2. This area represents all the points \( (x, y) \) that satisfy both inequalities.

### Final Answer

The solution set consists of all points in the overlapping shaded region on the graph.

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