substitution
Substitution is swapping a letter for what it stands for. If a formula says “distance = speed × time” and you are told the speed is 60 and the time is 2, you put those numbers in the place of the letters and read off distance = 60 × 2 = 120. You are filling in the blanks of a general statement to get a specific result.
More generally, you may substitute not only a number for a variable but one expression for another, provided they are equal. If you already know that y = x + 1, then anywhere y appears you may write x + 1 instead. This is the engine behind evaluating formulas, behind the substitution method for systems of equations, and behind change-of-variable tricks throughout mathematics.
The one rule to respect is consistency: a given letter must be replaced by the same value everywhere it appears within that step. If x = 5, then x^2 + x becomes 5^2 + 5 = 30 — both x’s get the 5. Substituting carelessly, or forgetting parentheses around a negative value, is a frequent source of arithmetic slips.
Evaluate 2x + y when x = 4 and y = −3: 2(4) + (−3) = 8 − 3 = 5.
Drop the numbers in for the letters, then do the arithmetic.
Always wrap a substituted negative in parentheses: with x = −2, x^2 means (−2)^2 = 4, not −2^2 = −4. The parentheses keep the sign attached to the squaring.