How can I guarantee the existence of a solution to this quadratic system of equations?

Question

I have $n$ real quadratic equations and $n$ real variables, $x_i$, of the following form:

$$\sum_{i\neq j} a_{ijk}x_ix_j+\sum_ib_{ik}x_i+c_k=0 \ \forall k$$

for $i,j,k\in\{1,\dots n\}$; all coefficients are real and I am interested in the existence of a real solution. Is there a condition on the coefficients to guaranty this?