Find the solutions to the system of nonlinear equations given by: \[ \left\{\begin{array}{l} y=-3 x+3 \\ y=-x^{2}+3 \end{array}\right. \]

Step 1 ：Set the two equations equal to each other: \(-3x + 3 = -x^2 + 3\)

Step 2 ：Solve the equation for x to get: \(x = 0\) and \(x = 3\)

Step 3 ：Substitute the x-values into one of the original equations to find the corresponding y-values: \(y = -3(0) + 3 = 3\) and \(y = -3(3) + 3 = -6\)

Step 4 ：The solutions to the system of nonlinear equations are \(\boxed{(0, 3)}\) and \(\boxed{(3, -6)}\)