Algebra 1 Unit 2 Flashcards

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Questions and Answers

What is a model?

A statistical representation of a problem (correct)

A type of mathematical equation

A method of problem solving

A specific solution to an equation

What is a constraint in a model?

A limitation on the possible values of variables in a model

What are equivalent equations?

Equations that have the exact same solutions

What forms a system of equations?

Two or more equations that represent the constraints in the same situation Signup and view all the answers

What is the solution to a system of equations?

A coordinate pair that makes both equations true Signup and view all the answers

What does substitution mean in algebra?

Replacing a variable with an expression it is equal to Signup and view all the answers

What is the elimination method?

A method of solving a system of equations where you eliminate one variable Signup and view all the answers

What are equivalent systems of equations?

Two systems that share the exact same solution set Signup and view all the answers

What forms a system of inequalities?

Two or more inequalities that represent constraints in the same situation Signup and view all the answers

What are solutions to a system of inequalities?

All pairs of values that make the inequalities true Signup and view all the answers

What is an equation in one variable?

An equation containing one unknown quantity Signup and view all the answers

What does standard form refer to in algebra?

Ax + By = C Signup and view all the answers

What is the slope-intercept form of a line?

y = mx + b Signup and view all the answers

What is a linear function?

A function where the output changes at a constant rate relative to the input Signup and view all the answers

What is the average rate of change?

A way to quantify how a quantity is changing over a particular interval Signup and view all the answers

What is a solution set?

The set of all values that make the equation or inequality true Signup and view all the answers

What characterizes a negative relationship between variables?

An increase in one variable occurs with a decrease in another Signup and view all the answers

What characterizes a positive relationship between variables?

Values of one variable increase as values of another variable increase Signup and view all the answers

Study Notes

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.

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Description

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.