`y - 2x le 1, x + y le 2, x ge 0, y ge 0 `

Explanation

To solve the system of linear inequalities given by:

1. \( y - 2x \leq 1 \)
2. \( x + y \leq 2 \)
3. \( x \geq 0 \)
4. \( y \geq 0 \)

we will use the graphical method. Here’s a step-by-step solution:

### Step 1: Convert inequalities to equations
First, we will convert the inequalities into equations to find the boundary lines.

1. From \( y - 2x = 1 \):
\[ y = 2x + 1 \]

2. From \( x + y = 2 \):
\[ y = 2 - x \]