Algebra 1 Unit 5 Flashcards

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Questions and Answers

What is a coefficient?

The sum of the variables in a product

The constant following the variables in a product

The constant added to the variables in a product

The constant preceding the variables in a product (correct)

What are consistent equations?

A system of linear equations that contain at least one common point.

What are dependent equations?

A system of linear equations that rely on each other for the algebraic or graphic form of the equation.

What is a determinant?

The value of (row 1, column 1)(row 2, column 2) - (row 1, column 2)(row 2, column 1) in a 2 by 2 matrix. Signup and view all the answers

What are inconsistent equations?

A system of linear equations that do not contain any common points. Signup and view all the answers

What are independent equations?

A system of linear equations that do not rely on each other for the algebraic or graphic form of the equation. Signup and view all the answers

What does infinitely many solutions mean?

A set of linear equations that coincide and share every point as a point of intersection. Signup and view all the answers

What is a linear inequality?

An open sentence of the form Ax + By + C < 0 or Ax + By + C > 0. Signup and view all the answers

What is a matrix?

A rectangular array made up of rows and columns. Signup and view all the answers

What does no solution indicate?

A set of parallel lines that will never share a point of intersection. Signup and view all the answers

What does one solution mean in a system of equations?

A set of linear equations that share a common point known as the point of intersection (x,y). Signup and view all the answers

What is the standard form of a linear equation?

The form Ax + By = C of a linear equation. Signup and view all the answers

What does substitute mean in algebra?

Replace a quantity with its equal. Signup and view all the answers

What is a system determinant?

The determinant found when column 1 consists of the x-coefficients and column 2 consists of the y-coefficients of a linear system. Signup and view all the answers

What is the x-determinant?

The determinant found when column 1 consists of the constants and column 2 consists of the y-coefficients of a linear system. Signup and view all the answers

What is the y-determinant?

The determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system. Signup and view all the answers

Study Notes

Algebra 1 Unit 5 Key Concepts

Coefficient: Refers to the constant factor that appears before variables in a product, essential for understanding polynomials and equations.
Consistent Equations: A system of linear equations that intersects at least once, indicating that there exists at least one solution.
Dependent Equations: These are systems where the equations are algebraically related, typically representing the same line graphically and yielding infinitely many solutions.
Determinant: A scalar value computed from a 2x2 matrix, calculated using the formula: (row 1, column 1)(row 2, column 2) - (row 1, column 2)(row 2, column 1), important for solving systems of equations.
Inconsistent Equations: Linear systems that do not have a point of intersection, meaning there are no solutions, often represented graphically as parallel lines.
Independent Equations: A system of equations that do not depend on one another for their algebraic or graphical representation, producing exactly one solution.
Infinitely Many Solutions: Occurs in scenarios where a set of linear equations coincide perfectly, hence every point on the line is a solution; this is both dependent and consistent.
Linear Inequality: An expression of the form Ax + By + C < 0 or Ax + By + C > 0, used to represent regions of solutions rather than specific points.
Matrix: A rectangular arrangement of numbers organized in rows and columns, often used in linear algebra to facilitate calculations.
No Solution: Represents scenarios where two lines in a system are parallel, implying they will never intersect; categorized as inconsistent.
One Solution: Occurs when two linear equations intersect at a single point, denoted as (x, y), which is both an independent and consistent solution.
Standard Form: The representation of a linear equation in the standard format Ax + By = C, highlighting the relationship between variables.
Substitute: A method used in algebra to replace a variable with an equivalent value or expression, useful in solving equations.
System Determinant: The determinant of a system created using x-coefficients in the first column and y-coefficients in the second column, aiding in solving systems of equations systematically.
X-Determinant: Derived from a linear system where the first column comprises constants and the second includes y-coefficients, useful for finding specific solutions within a system.
Y-Determinant: Similar to the X-Determinant, but uses x-coefficients in the first column and constants in the second to analyze linear systems.

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Test your understanding of key algebra concepts with these flashcards from Algebra 1 Unit 5. This quiz covers important terms such as coefficients, consistent equations, and determinants. Perfect for reinforcing your knowledge and preparing for exams.