Step 1 :The problem is asking to solve the system of equations. This means we need to find the values of x and y that satisfy both equations. We can solve this problem by graphing the two equations and finding their intersection points.
Step 2 :The system of equations is given by \[\begin{array}{l} y=\frac{1}{3} x+4 \\ y=x^{2}+4 x-2 \end{array}\]
Step 3 :We find the intersection points of these two equations, which are the solutions to the system of equations.
Step 4 :The solutions to the system of equations are \((-4.89, 2.37)\) and \((1.23, 4.41)\).
Step 5 :\[\boxed{\text{The solutions to the system of equations are } (-4.89, 2.37) \text{ and } (1.23, 4.41)}\]