System of Linear Equations and Inequality

Independent

A variable in an equation that may have its value freely chosen without considering values of any other variable. For equations such as y = 3x - 2, the independent variable is x. The variable y is not independent since it depends on the number chosen for x.

Dependent

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Inconsistent

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.

Consistent

In mathematics and in particular in algebra, a linear or nonlinear system of equations is consistent if there is at least one set of values for the unknowns that satisfies every equation in the system—that is, that when substituted into each of the equations makes each equation hold true as an identity.

Elimination

In order to use the elimination method, you have to create variables that have the same coefficient—then you can eliminate them. Multiply the top equation by 5. Next add the equations, and solve for y. Substitute y = 10 into one of the original equations to find x.

Substitution

Math definition of Substitution: Substitution - A strategy for solving systems of equations that include solving for one variable and using that solution to find the other variable.

System of Inequality

Solving Systems by Addition. A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables

System of Equation

Solving Systems by Addition. A "system" of equations is a set or collection of equations that you deal with all together at once. Linear equations (ones that graph as straight lines) are simpler than non-linear equations, and the simplest linear system is one with two equations and two variables.