Find the solution of the system of equations. \[ \begin{array}{l} 3 x-8 y^{4}=19 \\ 3 x+5 y=-46 \end{array} \]

Step 1 ：Step 1: Solve the second equation for \(x\): \[x = \frac{-5y - 46}{3}\]

Step 2 ：Step 2: Substitute this expression for \(x\) into the first equation: \[3\left(\frac{-5y - 46}{3}\right) - 8y^{4} = 19\]

Step 3 ：Step 3: Solve the resulting equation for \(y\), then find the corresponding \(x\) values: \[y \approx -1.9481, x \approx 12.2939\]