Singular

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As an economist who is not familiar with math and singular, I've been struggling to find a general way of solving the following type of problems. I really hope that someone can help me out.

Def: A_ij, B_j are n by n real-valued matrices - may well be singular.
Question: Solve for all solutions for (X1,X2) to the following system of multivariate matrix quadratic form using Groebner basis.

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A_11*X1^2 + A12*X2*X1 - X1 + B1 = 0;
A_21*X1*X2 + A22*X2^2 -X2 + B2 = 0;
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Ideally, I want to have a matlab code for this problem, only to fail. I used the built-in vpasolve.m. It didn't work.
So can anyone write a sample code for this in Singular and show how to run the code?

Solving this problem is so important to my research.
Thank you