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# Algebra 1 Unit 5 Flashcards

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### 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?

<p>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.</p> Signup and view all the answers

### What are inconsistent equations?

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

### What are independent equations?

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

### What does infinitely many solutions mean?

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

### What is a linear inequality?

<p>An open sentence of the form Ax + By + C &lt; 0 or Ax + By + C &gt; 0.</p> Signup and view all the answers

### What is a matrix?

<p>A rectangular array made up of rows and columns.</p> Signup and view all the answers

### What does no solution indicate?

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

### What does one solution mean in a system of equations?

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

### What is the standard form of a linear equation?

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

### What does substitute mean in algebra?

<p>Replace a quantity with its equal.</p> Signup and view all the answers

### What is a system determinant?

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

### What is the x-determinant?

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

### What is the y-determinant?

<p>The determinant found when column 1 consists of the x-coefficients and column 2 consists of the constants of a linear system.</p> 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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## Description

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.

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