https://file.aiquickdraw.com/mathbot/file/1725889553925sftnyy69.jpg

The graphical solution for the system of linear equations \(6x - y + 4 = 0\) and \(2x - 5y = 8\) is shown above. The region bounded by these lines and the y-axis is shaded in grey. 

### Steps to Interpret the Graph:
1. **Plotting the Lines:** 
   - The blue line represents the equation \(6x - y + 4 = 0\), which simplifies to \(y = 6x + 4\).
   - The green line represents the equation \(2x - 5y = 8\), which simplifies to \(y = \frac{2x - 8}{5}\).
  
2. **Intersection of Lines:**
   - The two lines intersect at the point where their \(x\) and \(y\) values are equal. You can solve this algebraically or find it graphically where the two lines cross.

3. **Shaded Region:**
   - The region bounded by the two lines and the y-axis is shaded. This area represents the solution set where the two inequalities intersect.

Would you like a detailed step-by-step solution on how to solve these equations algebraically? Or do you have any questions?

Here are some related questions to deepen your understanding:

1. How would you solve the system of equations algebraically instead of graphically?
2. What is the significance of the shaded region in this graph?
3. How can you determine the intersection point algebraically?
4. How would you describe the solution set if the system of equations had no intersection?
5. Can these equations be rewritten to identify their slopes and intercepts easily?

**Tip:** When solving graphically, always ensure that your scales on both axes are equal to accurately interpret intersection points and regions.

Solve the following pairs of linear equations graphically: 6x - y + 4 = 0 and 2x - 5y = 8. Shade the region bounded by the lines and the y-axis.

Graphically solve the pair of linear equations 6x - y + 4 = 0 and 2x - 5y = 8. Follow the steps to plot the lines, find the intersection, and shade the region bounded by the lines and the y-axis. Suitable for students in Grades 9-11 learning about linear equations and graphing.

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