STATEMENT-1 : In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. STATEMENT-2 : In an elastic collision, the linear momentum of the system is conserved.

Step 1: Analyze Statement-1.

For a perfectly elastic collision between two bodies of masses $m_1$ and $m_2$ with initial velocities $u_1, u_2$ and final velocities $v_1, v_2$, both linear momentum and kinetic energy are conserved.

The conservation of linear momentum gives:

$$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$$

The conservation of kinetic energy gives:

$$\frac{1}{2}m_1u_1^2 + \frac{1}{2}m_2u_2^2 = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2$$

Solving these two equations simultaneously yields:

$$v_2 - v_1 = u_1 - u_2$$

Taking the magnitude of the relative velocities:

$$|v_1 - v_2| = |u_1 - u_2|$$

This shows that the relative speed of separation after the collision is equal to the relative speed of approach before the collision. Thus, Statement-1 is true.

Step 2: Analyze Statement-2.

In any collision where no external force acts on the system, the total linear momentum is conserved.

$$p = \text{constant}$$

Thus, Statement-2 is true.

Step 3: Determine the relationship between the statements.

To derive the equality of relative speeds (Statement-1), both the conservation of linear momentum and the conservation of kinetic energy are required. For a general collision with coefficient of restitution $e$:

$$|v_1 - v_2| = e|u_1 - u_2|$$

Since linear momentum is conserved in all types of collisions (including inelastic collisions where $e < 1$), conservation of momentum alone does not guarantee the equality of relative speeds. Therefore, Statement-2 is not the correct explanation for Statement-1.

Answer: Statement-1 is true, Statement-2 is true; Statement-2 is NOT the correct explanation for Statement-1.