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College Algebra Flashcards

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Questions and Answers

What is a conditional equation?

An equation that has infinitely many solutions.

An equation that is always true for any value.

An equation that has no solution.

An equation that is true for some values of the variable but not for others. (correct)

What is a contradiction equation?

An equation that is always true.

An equation with infinitely many solutions.

An equation that has no solution. (correct)

An equation that can be solved easily.

What is an identity equation?

An equation that is always true for any value. (correct)

An equation that can be true for some values.

An equation that results in complex solutions.

An equation that has no solution.

What does the union symbol represent?

Uses 'or' Signup and view all the answers

What does the intersection symbol represent?

Uses 'and' Signup and view all the answers

What is the slope-intercept formula?

y = mx + b Signup and view all the answers

What is the slope formula?

y2 - y1 / x2 - x1 Signup and view all the answers

How can you tell if two lines are parallel by looking at their equations?

Same slope, different y-intercept Signup and view all the answers

How can you tell if two lines are perpendicular by looking at their equations?

Slopes (m) are opposite reciprocals Signup and view all the answers

How do you find the x-intercept?

Plug in 0 for y Signup and view all the answers

How do you find the y-intercept?

Plug in 0 for x Signup and view all the answers

What is a consistent system?

A system with at least one solution. Signup and view all the answers

What is an inconsistent system?

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

What is a dependent system?

A system with infinitely many solutions. Signup and view all the answers

What is an independent system?

A system with exactly one solution. Signup and view all the answers

Study Notes

Conditional Equation

True for certain values of the variable but not for others.

Contradiction Equation

An equation with no solution, exemplified by x = x + 1.

Identity Equation

An equation that holds true for any value assigned to the variable.

Union Symbol

Represented by "U" and indicates the use of "or."

Intersection Symbol

Denoted by an upside-down "U" and signifies the use of "and."

Slope-Intercept Formula

The formula to find the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

Slope Formula

Calculated as (y2 - y1) / (x2 - x1) to determine the steepness of a line.

Parallel Lines

To identify parallel lines in an equation, they must have the same slope but different y-intercepts.

Perpendicular Lines

Lines are perpendicular if their slopes (m) are opposite reciprocals of one another.

Finding the X-Intercept

To find the x-intercept of a function, set y to 0 and solve for x.

Finding the Y-Intercept

To find the y-intercept, set x to 0 and solve for y.

Consistent System

A system of equations or inequalities with at least one solution.

Inconsistent System

A system characterized by having no solutions at all.

Dependent System

A system of equations with infinitely many solutions due to matching lines.

Independent System

A system of equations that results in exactly one unique solution.

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Description

Test your understanding of key algebraic concepts with this set of flashcards. Each card features essential terms, including conditional equations, contradiction equations, and identity equations. Perfect for mastering the fundamentals of college-level algebra.