Linear Equations Vocabulary Flashcards

Vocabulary flashcards covering fundamental definitions, properties, and types of linear equations.

Equation

A statement that two expressions are equivalent or equal.

Member of the equation

The expression on each side of the equality sign.

Unknown

A variable in an equation.

Solution (or Root)

A number that produces a true statement when substituted for the variable in an equation.

Solution set

The set of all roots for an equation.

Inconsistent equation

An equation that has no solution.

Identity equation

An equation that is true for any number substituted to the variable.

Conditional equation

An equation that is true only for certain values of the unknown.

Addition Property of Equality

For all real numbers $a$, $b$, and $c$, if $a = b$ then $a + c = b + c$.

Subtraction Property of Equality

For all real numbers $a$, $b$, and $c$, if $a = b$ then $a - c = b - c$.

Multiplication Property of Equality

For all real numbers $a$, $b$, and $c$, if $a = b$ then $a \times c = b \times c$.

Division Property of Equality

For all real numbers $a$, $b$, and $c$, if $a = b$ then $\frac{a}{c} = \frac{b}{c}$.

Equivalent equations

Equations that have the same solution sets.

Linear equation

An equation that can be written in the form $ax + b = 0$, where $a$ and $b$ are real numbers and $a \neq 0$.

Extraneous root

A root of the derived equation but not the root of the original equation.