Solve the System of Equations: x + y = 15, 2x + 2y = 12

Choose the correct answer for the following exercise:

$\begin{cases} x+y=15 \\ 2x+2y=12\frac{}{} \end{cases}$

To solve the system of equations, follow the steps below:

• Simplify the second equation: Start with $2x + 2y = 12$. Divide every term by 2 to simplify it to $x + y = 6$.
• Compare the two equations now: $x + y = 15$ and $x + y = 6$.

Consider these equations:
Since both are simplified to the form $x + y = \text{constant}$, they describe two parallel lines, given that they have the same coefficients of $x$ and $y$ but different constants (15 and 6).

Parallel lines never intersect. Thus, there is no solution for this system of equations, as they represent two distinct parallel lines.

Therefore, the correct answer is: No solution.