Algebra 1 Unit 4 Flashcards

Questions and Answers

What is the definition of intersection?

A group of similar and related elements considered together.

An equation whose graph is a straight line.

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

The point that two lines have in common. (correct)

What is a linear equation?

An equation whose graph is a straight line.

What is a system in mathematics?

A group of similar and related elements considered together.

What is the solution of a linear equation?

An ordered pair (x, y) that satisfies all the equations in the system. Signup and view all the answers

Substitution is a method of solving systems of linear equations by ______.

substituting an expression for a variable. Signup and view all the answers

What is Gaussian elimination?

A method of solving systems of linear functions by adding equations together. Signup and view all the answers

What does it mean for lines to coincide?

To occupy the same space at the same time. Signup and view all the answers

What is a consistent system?

A system of linear equations that has at least one solution. Signup and view all the answers

What is a dependent system?

A system of linear equations with an infinite number of solutions. Signup and view all the answers

What is an inconsistent system?

A system of linear equations that has no solution. Signup and view all the answers

What is an independent system?

A system of linear equations that has exactly one solution. Signup and view all the answers

What is a linear inequality?

A relation where the expression on one side does not equal the expression on the other side. Signup and view all the answers

What is a system of linear inequalities?

A set of two or more linear inequalities considered together. Signup and view all the answers

Study Notes

Algebra 1 Unit 4 Concepts

Intersection: Refers to the specific point where two lines cross or meet.
Linear Equation: Represents a relationship where the graph forms a straight line, typically expressed in the form Ax + By = C.
System: A collection of similar and related elements that are analyzed together to understand relationships.

Solutions and Systems of Linear Equations

Solution of a Linear Equation: An ordered pair (x, y) that fulfills the conditions of all equations present in a system.
Substitution Method: A technique for solving systems of linear equations; it involves substituting one variable with an expression derived from another equation before solving for the remaining variable.
Gaussian Elimination: A systematic method for solving systems of linear functions, achieved through adding or manipulating equations to eliminate variables.

Types of Systems

Coincide: When two lines share all points in common; such lines are termed coincident.
Consistent System: A linear equation system that has at least one solution, indicating that the equations intersect at least at one point.
Dependent System: Defines a system of linear equations that yields an infinite number of solutions, meaning the equations represent the same line.
Inconsistent System: Characterizes a linear equation system that has no solution, implying the lines are parallel and never intersect.
Independent System: An assortment of linear equations that has precisely one solution, indicating the lines intersect at a single point.

Inequalities

Linear Inequality: A mathematical statement involving a linear expression that is not equal to another; can be represented with inequality symbols (e.g., Ax + By > C).
System of Linear Inequalities: Consists of two or more linear inequalities evaluated together to determine the feasible region for solutions.

Description

Test your knowledge of key concepts in Algebra 1, specifically focusing on Unit 4 vocabulary. This set of flashcards covers important terms such as intersection, linear equations, and solutions. Perfect for students looking to reinforce their understanding of algebraic concepts.