Blakley's scheme was introduced at the same time as Shamir's.
Blakley’s Secret Sharing Scheme (SSS) uses hyperplane geometry to solve the secret sharing problem. The secret is a point in a $t$ dimensional space and the $n$ shares are affine hyperplanes
that pass through this point. An affine hyperplane in a
$t-$dimensional space with coordinates in a field $F$ can be
described by a linear equation of the following form:
$$
a_1x_1 + a_2x_2 + \cdots + a_tx_t = b.
$$
The intersection point is obtained by finding the intersection of any $t$ of these hyperplanes. The secret can be
any of the coordinates of the intersection point or any
function of the coordinates.
Appendix:
In fact, Shamir scheme is based on Reed-Solomon not Reed-Muller codes. One could even say that Shamir rediscovered the Reed-Solomon codes, in the context of "erasure of symbols" (missing codeword coordinates).
To make that precise, it is possible to think of Reed-Solomon codewords $c_f,$ in terms of the evaluations of a polynomial over the nonzero elements of a finite field (usually termed Generalized Reed-Solomon formulation):
$$
c_f=(f(x_1),f(x_2),\ldots,f(x_n))_{x_i \in \mathbb{F}_q\setminus\{0\}}
$$
and if $f$ has degree $k$ then any $k+1$ coordinates are enough to recover the correct polynomial. Then $f(0)$ is used to recover the secret $s$. The polynomial is defined by $f(0)=s,$ and its other coefficients are randomly uniformly chosen.
The point is the collection
$$
\{c_f: deg(f)\leq k-1\}
$$
is precisely the set of Reed-Solomon codewords for the Reed Solomon code of dimension $k$ and minimum distance $n-k+1$ over $\mathbb{F}_q.$ It's just that one does not transmit the full codeword $c_f$ but use a subcollection
$$
\{f(x_1),f(x_2),\ldots,f(x_{k+1})\}
$$
as the shares.