The system of equations given is:

1. $y = 4x - 2$ (green line)
2. $y = -x + 3$ (blue line)

The solution to a system of linear equations graphically is where the two lines intersect. From the graph, it looks like the two lines intersect at the point $(1, 2)$.

Thus, the solution is:

• $X = 1$
• $Y = 2$

Would you like further details on how to verify this solution algebraically or any other assistance? Here are five related questions for you to consider:

1. How do you solve a system of linear equations algebraically?
2. What are the methods for solving a system of equations graphically?
3. How can you verify if a point is a solution to a system of equations?
4. What does it mean if two lines on a graph do not intersect?
5. How can substitution be used to solve a system of equations?

Tip: Always double-check your solution by substituting the values back into the original equations to ensure they satisfy both.