Question

Vocabulary words
Definition or Description


Lesson 2: Equations in Two Variables
equation




solution




ordered pair




solution set




variable




Lesson 3: Creating Two-Variable Equations
constant




domain




range


continuous data




discreet data


dependent variable




independent variable


inequality




rate of change (slope)




x-intercept




y-intercept


Lesson 4: Inequalities in Two Variables
strict inequality




Lesson 5: Solution Sets of Simultaneous Equations
parallel line




quadratic equation




system of equations




Lesson 6: Solving Simultaneous Equations Using Substitution
substitution




Lesson 7: Solving Simultaneous Equations Using Elimination
elimination method




equivalent systems




Lesson 8: Solution Sets of Simultaneous Inequalities
linear inequality




system of inequalities

Answer 1

Here are concise definitions/descriptions for each vocabulary word:

- equation: A mathematical statement that two expressions are equal, often containing variables (e.g., 2x + 3 = 7).
- solution: A value (or ordered pair) that makes an equation or inequality true.
- ordered pair: A pair of numbers written as (x, y) that gives the coordinates of a point in the plane.
- solution set: The collection of all solutions to an equation, inequality, or system (for two variables, a set of ordered pairs).
- variable: A symbol (usually a letter) that represents an unknown or changeable quantity.
- constant: A fixed value that does not change.
- domain: The set of all possible input values (usually x-values) for a relation or function.
- range: The set of all possible output values (usually y-values) produced by a relation or function.
- continuous data: Data that can take any value within an interval (unbroken), typically represented by continuous curves.
- discrete data: Data that take distinct, separate values (often integers or counts); not continuous.
- dependent variable: The variable whose value depends on another variable (commonly y).
- independent variable: The variable that determines the value of the dependent variable (commonly x).
- inequality: A statement comparing two expressions using <, >, ≤, or ≥.
- rate of change (slope): The change in the dependent variable divided by the change in the independent variable; for a line, slope = (y2 − y1) / (x2 − x1).
- x-intercept: The point where a graph crosses the x-axis (y = 0), written as (a, 0).
- y-intercept: The point where a graph crosses the y-axis (x = 0), written as (0, b).
- strict inequality: An inequality that uses only < or > (not ≤ or ≥), excluding equality.
- parallel line: Two lines in the same plane that never meet; they have the same slope (but different intercepts).
- quadratic equation: A polynomial equation of degree 2, typically ax^2 + bx + c = 0, where a ≠ 0.
- system of equations: Two or more equations considered together; solutions satisfy all equations simultaneously.
- substitution: A method for solving systems where you solve one equation for a variable and substitute that expression into the other equation(s).
- elimination method: A method for solving systems by adding or subtracting equations to eliminate one variable so the other can be solved.
- equivalent systems: Different systems of equations that have the same solution set.
- linear inequality: An inequality that involves a linear expression (e.g., ax + by ≤ c); its graph is a half-plane in two variables.
- system of inequalities: Two or more inequalities considered together; the solution is the intersection of their individual solution regions.

If you’d like, I can add examples or simple diagrams for any of these.