# Function usolveAll Finds all solutions of a linear equation system by backward substitution. Matrix must be an upper triangular matrix. `U * x = b` ## Syntax ```js math.usolveAll(U, b) ``` ### Parameters Parameter | Type | Description --------- | ---- | ----------- `U` | Matrix, Array | A N x N matrix or array (U) `b` | Matrix, Array | A column vector with the b values ### Returns Type | Description ---- | ----------- DenseMatrix[] | Array[] | An array of affine-independent column vectors (x) that solve the linear system ## Examples ```js const a = [[-2, 3], [2, 1]] const b = [11, 9] const x = usolveAll(a, b) // [ [[8], [9]] ] ``` ## See also [usolve](usolve.md), [lup](lup.md), [slu](slu.md), [usolve](usolve.md), [lusolve](lusolve.md)