Solve the Equation System: 2x - 2y = 10 and 4x - 4y = 32

We start by analyzing the given system of equations:

The first equation is $2x - 2y = 10$.

The second equation is $4x - 4y = 32$.

To determine the relationship between these two lines, let's simplify both equations.

1. Simplify the first equation:
Divide every term by 2:
$x - y = 5$.

2. Simplify the second equation:
Divide every term by 4:
$x - y = 8$.

Notice that after simplification, we have:

• First equation: $x - y = 5$
• Second equation: $x - y = 8$

Upon comparison, both equations simplify to lines with the same slope but different intercepts. Therefore, they represent two parallel lines that do not intersect.

Consequently, the system of equations has no solution since parallel lines never meet.

Therefore, the correct answer is: No solution.