  In arXiv:2203.03372 we presented a modification of 11-dimensional
supergravity field equations which upon dimensional reduction yields
generalized supergravity equations in 10-dimensions. In this paper we provide
full technical details of that result which is based on SL(5) exceptional field
theory. The equations are obtained by making a non-unimodular tri-vector
Yang-Baxter deformation which breaks the initial GL(11) symmetry down to
GL(7)xGL(4). We also give some non-trivial solutions to these equations.
