7. \( \left\{\begin{array}{l}\frac{1}{4}(y-3)=-x \\ y=-4 x+3\end{array}\right. \)

To solve the system of equations, let's first rewrite the equations in a more manageable form. The first equation, \(\frac{1}{4}(y-3)=-x\), can be simplified to \(y - 3 = -4x\) or \(y = -4x + 3\). Coincidentally, this is the same as the second equation! This tells us that both equations represent the same line in a two-dimensional space. Therefore, the set of solutions is not just a single point but rather every point along the line given by the equations, which can be expressed as \(-4x + 3\). Thus, the solution can be described as all ordered pairs \((x, -4x + 3)\) for any value of \(x\). In summary, infinitely many solutions exist, encapsulated by the equation \(y = -4x + 3\).