1) \( \begin{aligned} 4 x+y & =30 \\ 2 x-y & =12\end{aligned} \)

To solve the system of equations, we can use the substitution or elimination method. Let's use the elimination method for a twist of fun! First, let's add the two equations together to eliminate \(y\): 1) \(4x + y = 30\) 2) \(2x - y = 12\) By adding them, we get: \(4x + y + 2x - y = 30 + 12\) This simplifies to: \(6x = 42\) Now, dividing by 6 gives us: \(x = 7\) Plugging \(x = 7\) back into the first equation \(4(7) + y = 30\): \(28 + y = 30\) This leads to: \(y = 2\) So, the solution to the system is \(x = 7\) and \(y = 2\). If you want fun in your math, just remember those clever eliminations can sometimes lead to unexpected discoveries, just like hidden gems in a treasure hunt! Exploring further into systems of equations can even lead to topics like matrices and determinants which add more tools to your math toolbox for multidimensional adventures!