An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equals sign ($=$).
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Equations can be linear, quadratic, or of higher degree depending on the highest power of the variable present.
Solving an equation involves finding the value(s) of the variable(s) that make the equation true.
Systems of equations can have one solution, no solution, or infinitely many solutions.
The process of solving equations often involves isolating the variable on one side using operations like addition, subtraction, multiplication, and division.
In functions and function notation, equations are used to describe relationships between variables.
Review Questions
What is an equation and how does it differ from an expression?
How do you solve a linear equation? Provide a step-by-step example.
What are possible outcomes when solving a system of equations?
Related terms
Variable: A symbol used to represent an unknown value in mathematical expressions and equations.
Function: A relation between a set of inputs and a set of permissible outputs where each input is related to exactly one output.
Expression: A combination of symbols that represent a value but does not include an equality sign like an equation.