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 Solving System of Equations Graphically
Concept

System of Equations

A system of equations is a set of two or more equations involving the same variables. The solutions to a system are values for these variables that satisfy all the equations simultaneously. The most common systems are systems of linear equations, which contain only linear equations. A system of equations is usually written as a vertical list with a curly bracket on the left-hand side.
Graphically, solutions to systems of equations are the points where the graphs of the equations intersect. For this reason, these solutions are usually expressed as coordinates. Since the graphs of linear equations are lines, they can have or infinitely many points of intersection. Therefore, the number of solutions for a linear system is also or infinitely many solutions.
Number of solutions to a linear system
Systems can contain many different types of equations. Systems of equations can be solved graphically or algebraically.

Extra

Types of System of Equations

Systems of equations can be classified based on their algebraic characteristics, especially the types of equations involved. The following are some of the most common types.

Type of System Description Example
Linear System Includes only linear equations.
Linear-Quadratic System Includes one linear equation and one quadratic equation.
Quadratic System Consists solely of quadratic equations.
Nonlinear System Contains at least one nonlinear equation.

Keep in mind that linear-quadratic systems and quadratic systems are also nonlinear systems.

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