Does the system of linear equations showm below have a solution? Explain. \[ \left\{\begin{array}{l} \frac{3}{4} x-3=y \quad y \geq \frac{1}{4} \\ 4 x-3 y=5 \end{array}\right. \]

To determine if the system of linear equations has a solution, we can analyze the equations one by one. The first equation \(\frac{3}{4} x - 3 = y\) can be rewritten to express \(y\) in terms of \(x\), giving \(y = \frac{3}{4} x - 3\). The second equation \(4x - 3y = 5\) can also be rearranged to express \(y\) as \(y = \frac{4}{3} x - \frac{5}{3}\). The next step is to set the two expressions for \(y\) equal to each other to find \(x\). Solving \(\frac{3}{4} x - 3 = \frac{4}{3} x - \frac{5}{3}\) leads us to a common variable value. However, we should also ensure that any solution satisfies the additional constraint \(y \geq \frac{1}{4}\). After solving for \(x\), plugging it back into one of the equations will yield a \(y\) value. If this \(y\) is greater than or equal to \(\frac{1}{4}\), then the system has a solution; otherwise, it does not. This means to visualize the solution, you can graph the lines represented by both equations in Cartesian coordinates. The point of intersection gives the solution to the system, and you need to verify if this point meets the specified inequality. If they intersect within the valid range, there is a solution; if not, then no solution exists!