`{:(3x - y - 2 - 0),(2x + y - 8 = 0):}`

Answer

To solve the system of equations graphically, we will follow these steps:

### Given Equations:
1. \( 3x - y - 2 = 0 \)
2. \( 2x + y - 8 = 0 \)

### Step 1: Rewrite the equations in slope-intercept form (y = mx + b)

**For the first equation:**
\[ 3x - y - 2 = 0 \implies -y = -3x + 2 \implies y = 3x - 2 \]

**For the second equation:**
\[ 2x + y - 8 = 0 \implies y = -2x + 8 \]

### Step 2: Find the points for the first equation \( y = 3x - 2 \)

- **When \( y = 0 \):**
\[ 0 = 3x - 2 \implies 3x = 2 \implies x = \frac{2}{3} \]
Point: \( \left(\frac{2}{3}, 0\right) \)

- **When \( x = 0 \):**
\[ y = 3(0) - 2 \implies y = -2 \]
Point: \( (0, -2) \)

### Step 3: Find the points for the second equation \( y = -2x + 8 \)

- **When \( y = 0 \):**
\[ 0 = -2x + 8 \implies 2x = 8 \implies x = 4 \]
Point: \( (4, 0) \)

- **When \( x = 0 \):**
\[ y = -2(0) + 8 \implies y = 8 \]
Point: \( (0, 8) \)

### Step 4: Plot the points on a graph

- For the first equation, plot the points \( \left(\frac{2}{3}, 0\right) \) and \( (0, -2) \).
- For the second equation, plot the points \( (4, 0) \) and \( (0, 8) \).

### Step 5: Draw the lines

- Draw a line through the points of the first equation.
- Draw a line through the points of the second equation.

### Step 6: Find the intersection point

- The intersection point of the two lines is the solution to the system of equations.

### Step 7: Determine the coordinates of the intersection point

From the graphical representation, we find that the intersection point is \( (2, 4) \).

### Final Solution:
The solution to the system of equations is:
\[ x = 2, \quad y = 4 \]

---