Algebraic equations and systems of equations

An algebraic equation is an equality involving variables and constants, combined using addition, subtraction, multiplication, division, and powers. Solving the equation means finding all values of the variables that make the equation true. A system of equations is a collection of two or more equations with the same set of variables. The solution to a system is a set of variable values that satisfy all equations at once.

Important properties

• Equations can be linear (degree 1), quadratic (degree 2), or higher degree.

• Systems can be solved by substitution, elimination, or graphical methods.

• A system may have one solution, no solution, or infinitely many solutions.

• Checking solutions by substitution is essential.