To substitute
means to replace one thing by another. Substitution is the process
of replacing the letters in a formula by numbers. For example, the
surface area A cm^{2} of a cylinder of radius 5cm and height 12 cm
can be calculated by substituting 5 for r and 12 for h in the formula
A = 2 π r (r + h)

A = 2 π x 5 x (5 + 12) = 170 π

But substitution
can also involve substituting one algebraic expression for another.
For example, if a shoe box has dimensions a, b and c and it is required
to find the length of the diagonal PQ, then by Pythagoras theorem

PQ^{2} = PR^{2} + RQ^{2}

But PR^{2} = a^{2} + b^{2}

And RQ = c

So substituting for PR and RQ

PQ^{2} = a^{2} + b^{2} + c^{2}

from which