For a set of coplanar forces to be in equilibrium, the algebraic sum of the forces in both horizontal and vertical directions must be equal to zero. This means that the net force acting on the system in the horizontal direction is zero, and the net force acting in the vertical direction is also zero.

Mathematically, the conditions of equilibrium for coplanar forces can be expressed as:

$$\Sigma F_x = 0$$

$$\Sigma F_y = 0$$

Where:

- $$\Sigma F_x$$ represents the algebraic sum of all the forces acting in the horizontal direction.

- $$\Sigma F_y$$ represents the algebraic sum of all the forces acting in the vertical direction.

If these two conditions are satisfied, then the set of coplanar forces is said to be in equilibrium, meaning that the system will not experience any net movement or rotation.