Substitution

Substitution means replacing a variable with a number or another expression. If $y = 3x + 2$ and $x = 5$, you substitute $5$ for $x$ to get $y = 3(5) + 2 = 17$.

This is how you verify solutions. If you think $x = 4$ solves $2x + 1 = 9$, substitute and check: $2(4) + 1 = 8 + 1 = 9$. It works.

In algorithm analysis, you substitute input size $n$ into time complexity formulas to estimate runtime. If $T(n) = 2n^2 + 3n$, then $T(100) = 20000 + 300 = 20300$ operations.