Solve the Linear System: Find Solutions for x/2 + y = 3, x + 2y = 6

To solve this problem, we'll follow these steps:

• Step 1: Express one equation in terms of a single variable.
• Step 2: Substitute into the other equation.
• Step 3: Evaluate and determine the solution type.

Now, let's work through each step:
Step 1: Solve the first equation for $x$:
$\frac{x}{2} + y = 3 \quad \Rightarrow \quad x = 6 - 2y$.

Step 2: Substitute $x = 6 - 2y$ into the second equation:
$x + 2y = 6 \quad \Rightarrow \quad (6 - 2y) + 2y = 6$.

Step 3: Simplifying equation:
$6 - 2y + 2y = 6 \quad \Rightarrow \quad 6 = 6$.

This equation $6 = 6$ is always true, indicating that both equations are dependent and represent the same line.

Therefore, the system has infinite solutions.