Definitions: Systems of Equations

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This is a collection of definitions on the topic of Systems of Equations.

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Break-Even Analysis. A system of equations that looks at revenue vs. costs for a business. The solution is the break-even point.

Dependent System. A linear system in which the equations result in one graph, with an infinite number of solutions.

Graphical Solution to a Linear System. Where the graphs of a linear system intersect is the solution to the linear system. If there is no intersection, there is no solution.

Independent System. A linear system in which the equations result in two independent graphs that intersect at one point.

Inconsistent System. A linear system in which the equations result in parallel lines with no solution.

Linear System. A collection of linear equations, where the number of equations matches the number of variables, allowing for an algebraic solution.

Non-Linear Systems. A non-linear system consists of at least one non-linear function. The solution (if there is one) is where the graphs intersect.

Solving a Linear System Using Elimination. Combining the equations of a linear system in such a way as to remove enough variables to solve the system.

Solving a Linear System Using Matrices. Rewriting a linear system as the product of matrices allows for finding the solution to the system by finding the inverse of the coefficient matrix.

Solving a Linear System Using Substitution Taking the value for y from one linear equation and substituting it into the second equation to solve for x.

Solution to a System. A system of linear equations has a solution if there is an intersection point.

Simultaneous Equations. A system of equations is sometimes referred to as a set of simultaneous equations.