Algebra 1 Unit 2 Flashcards

Mathematical Concepts

• Model: Represents real-world problems mathematically or statistically, aiding in problem-solving and decision-making across various fields.
• Constraint: Limits the possible values of variables in a model, often defined by equations or inequalities (e.g., d≥0 for distance).
• Equivalent Equations: Equations yielding the same solutions, crucial for algebraic problem-solving.

Systems of Equations

• System of Equations: Consists of multiple equations that reflect constraints within a single situation, often represented with curly brackets.
• Solution to a System of Equations: The coordinate pair that satisfies all equations in the system; graphically represented by the intersection point of the equations.

Algebraic Techniques

• Substitution: Method of replacing a variable in an equation with an expression that it equals, simplifying the equation.
• Elimination: Technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

Systems of Inequalities

• Equivalent Systems: Two systems are equivalent if they have identical solution sets.
• System of Inequalities: Comprises multiple inequalities defining constraints of the same situation, with solutions represented by overlapping regions on a graph.
• Solutions to a System of Inequalities: All value pairs satisfying the inequalities, visualized as the intersection area of their graphs.

Equation Types

• Equation in One Variable: Involves a single unknown or variable, focusing on direct relationships.
• Standard Form: Linear equations written as Ax + By = C.
• Slope-Intercept Form: y = mx + b; m is the slope, b is the y-intercept, making it easy to graph linear equations.

Functions and Relationships

• Linear Function: Exhibits a constant rate of change in output relative to input, forming straight lines on a graph.
• Average Rate of Change: A measure indicating how a quantity varies across a specific interval, useful in analyzing functional behavior.

Relationships Between Variables

• Solution Set: All variable values that satisfy an equation or inequality, determining potential solutions.
• Negative Relationship: Occurs when an increase in one variable correlates with a decrease in another, indicating an inverse relationship.
• Positive Relationship: Shows that as one variable increases, so does the other, reflecting a direct correlation.

Test your knowledge of key concepts in Algebra 1 Unit 2 with these flashcards. This quiz covers important terms such as 'model' and 'constraint', and their definitions as related to mathematical problem-solving.