Key Terms in Algebra

Study Notes

Key Terms in Algebra

Infinite Solutions: Occurs when every point on one line intersects all points on another line, indicating that the two lines are essentially the same.
Coincide: Describes two graphs that share all their points, meaning they represent the same equation or relationship.
Elimination Methods: A strategy for solving systems of equations by adding or subtracting two equations to remove one variable, making it easier to solve.
Equal Values Method: Involves setting two equations equal to each other when both are equal to the same variable, allowing for the solution of one variable in terms of another.
Equation: A mathematical statement asserting the equality of two expressions, often involving variables.
Graph: A visual representation of numerical data that illustrates the relationships between variables.
Let Statement: A declaration at the beginning of a problem that identifies which variable will represent a specific quantity in subsequent equations.
No Solution: Describes a scenario where two lines are parallel and do not intersect, indicating that there is no set of values that satisfy both equations.
Mathematical Sentence: An equation that includes variables to represent unknown values and relations.
Model: A mathematical framework that summarizes a trend in data, useful for comparison, description, and prediction.
y = mx + b: This equation represents the slope-intercept form of a line, where 'm' is the slope, and 'b' is the y-intercept.
Parallel Lines: Two lines positioned in the same plane that do not meet, remaining equidistant from one another.
Point of Intersection: The specific coordinates where two graphs meet, indicating the solution for their corresponding equations.
Table: A structured way to present numerical data by organizing it into rows and columns for easy reference and analysis.
Situation: Refers to a context involving two or more equations that share the same variables.
System of Equations: A collection of equations involving the same set of variables, which can be solved together to find common solutions.
Solution: The specific value(s) that make an equation true, representing the point(s) of intersection in a graphical context.
Substitution Method: A technique for solving equations that entails substituting one variable with an expression derived from the other variable.
Standard Form of A Line: Represented by the formula ax + by = c, where 'a', 'b', and 'c' are constants specifying the line's properties in a more general format.