Solving a non-linear system with 3 variables (kinematics)

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I'm trying to find the parametric solutions for a 2-dimensional set of kinematics equations.

My params are:

  • Δx, Δy - initial and target positions.
  • Vx, Vy - initial velocity.
  • A - the acceleration magnitude.

My variables are:

  • t - time to reach x1, y1.
  • Ax - acceleration in the x axis.
  • Ay - acceleration in the y axis.

Given this and the kinematic equations I have this set:

$$ \left\{ \begin{array}{l} a_x^{2}+a_y^2=A^2 \\ Δx = v_xt + a_xt^2 \\ Δy = v_yt + a_yt^2 \end{array} \right. $$

I can't seem to find a technic to solve this set. Even when putting this in Wolfram Alpha with the parameters, it doesn't provide me a solution.

Is there even a way to solve this? Thanks.