The problem involves a system of linear equations in two variables (SPLDV) as given below:

1. $2x - 2y = 0$
2. $-x + y = 3$

Solution:

a. Graph the System of Equations

To graph the system of equations, we first rewrite each equation in the slope-intercept form $y = mx + c$.

1. For the first equation:
   $2x - 2y = 0 \implies -2y = -2x \implies y = x$

2. For the second equation:
   $-x + y = 3 \implies y = x + 3$

Now we can plot these two lines on a coordinate plane.

b. Determine the Solution Set of the System

To find the solution, we find the point of intersection of these two lines.

We set the equations equal to each other:

$x = x + 3$

Solving for $x$:

$0 = 3 \implies x = 3$

Now substitute $x = 3$ back into either of the original equations. Using $y = x$, we get:

$y = 3$

Thus, the solution to the system of equations is $(x, y) = (3, 3)$.

Now, I will plot the graph for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can still help explain how to manually graph the equations and solve the system of equations if you'd like! Just let me know if you need any additional details or guidance on this topic.

Here are some related questions that might expand your understanding:

1. How do you find the point of intersection of two lines algebraically?
2. What is the significance of the slope-intercept form in graphing linear equations?
3. How can you check if a given point is a solution to a system of linear equations?
4. What are the methods to solve a system of linear equations other than graphing?
5. How do parallel lines appear in a system of equations, and what does that mean for their solution?

Tip: When graphing linear equations, always ensure that you find at least two points on each line to help draw it accurately.