`2x + y ge 6, x + 2y ge 8, x ge 0, y ge 0`

Explanation

To solve the given system of linear inequalities graphically, we will follow these steps:

### Step 1: Convert inequalities to equations
We start by converting the inequalities into equations to find the boundary lines:
1. \(2x + y = 6\)
2. \(x + 2y = 8\)

### Step 2: Find intercepts for the first equation
For the equation \(2x + y = 6\):
- **When \(x = 0\)**:
\[ 2(0) + y = 6 \implies y = 6 \]
So, the y-intercept is \((0, 6)\).

- **When \(y = 0\)**:
\[ 2x + 0 = 6 \implies 2x = 6 \implies x = 3 \]
So, the x-intercept is \((3, 0)\).

### Step 3: Find intercepts for the second equation
For the equation \(x + 2y = 8\):
- **When \(x = 0\)**:
\[ 0 + 2y = 8 \implies 2y = 8 \implies y = 4 \]
So, the y-intercept is \((0, 4)\).

- **When \(y = 0\)**:
\[ x + 2(0) = 8 \implies x = 8 \]
So, the x-intercept is \((8, 0)\).

### Step 4: Plot the lines on a graph
Now we plot the points we found:
- For \(2x + y = 6\), plot the points \((0, 6)\) and \((3, 0)\).
- For \(x + 2y = 8\), plot the points \((0, 4)\) and \((8, 0)\).

### Step 5: Draw the lines
Draw the lines for both equations:
- The line for \(2x + y = 6\) will pass through \((0, 6)\) and \((3, 0)\).
- The line for \(x + 2y = 8\) will pass through \((0, 4)\) and \((8, 0)\).

### Step 6: Determine the shaded regions
Since the inequalities are "greater than or equal to," we will shade the region above both lines:
- For \(2x + y \geq 6\), shade above the line.
- For \(x + 2y \geq 8\), shade above this line as well.

### Step 7: Identify the feasible region
The feasible region is the area where the shaded regions for both inequalities overlap. This region represents all the possible solutions to the system of inequalities.

### Conclusion
The solution to the system of inequalities is the set of all points in the overlapping shaded area on the graph.

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