Definition of Terms - Pre-Calculus

System of Equations

A set of two or more equations solved at the same time.

Linear Equation

An equation whose graph is a straight line (example: ax + by = c).

Non-Linear Equation

An equation whose graph is not a straight line (quadratic, exponential, etc.).

Solution of a System

A pair (x, y) that satisfies all equations in the system.

Substitution Method

Solve one equation for a variable, then substitute in the other.

Elimination Method

Add or subtract equations to eliminate a variable.

Arithmetic Sequence

A sequence with a constant difference (d).

Common Difference (d)

d = a₂ – a₁

General Term

an = a₁ + (n – 1)d

Arithmetic Series

Sum of terms in an arithmetic sequence.

Sum Formula

Sn = n/2 (a₁ + an) or Sn = n/2 [2a₁ + (n – 1)d]

Geometric Sequence

A sequence where each term is multiplied by a constant ratio (r).

Common Ratio (r)

r = a₂ / a₁

General Term

an= a₁(rⁿ⁻¹)

Geometric Series

Sum of geometric sequence terms.

Finite Sum Formula

Sn = a₁(1 – rⁿ) / (1 – r)

Linear + Quadratic

y = x + 3 and y = x²

Quadratic + Quadratic

x² + y² = 25 and x² – y² = 9

Circle + Line

x² + y² = 16 and y = 2x