Denoting L as liquid and M as solid in a phase-diagram with the subscripts representing
different phases, a eutectoid reaction is described by

The correct option is: M₁ → M₂ + M₃

To understand why this is the correct representation, let us break down the phase reactions in material science and metallurgy:

In a phase diagram, phase transformations that occur at constant temperature (isothermal reactions) are characterized by the types of phases involved. The prompt denotes:
L as the liquid phase
M (specifically M₁, M₂, and M₃) as different solid phases.

Let us define the primary three-phase invariant reactions upon cooling:

1. Eutectic Reaction:
A single liquid phase transforms into two distinct solid phases.
$L\to M_1+M_2$

2. Eutectoid Reaction:
A single solid phase transforms into two distinct solid phases. The suffix -oid indicates that the reaction is similar to a eutectic reaction, but starts from a solid phase rather than a liquid phase.
$M_1\to M_2+M_3$

3. Peritectic Reaction:
A liquid phase and a solid phase react to form a single new solid phase.
$L+M_1\to M_2$

4. Peritectoid Reaction:
Two distinct solid phases react to form a third, single new solid phase.
$M_1+M_2\to M_3$

Therefore, based on the definitions, a eutectoid reaction is described by one solid phase transforming into two other solid phases:
$M_1\to M_2+M_3$