3 Variable Systems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the set of values that satisfy all equations simultaneously.

Front

What does it mean to solve a system of equations by elimination?

Back

Solving by elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variables.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

Front

What is a three-variable system?

Back

A three-variable system consists of three equations with three unknowns, typically represented as x, y, and z.

Front

How do you represent a solution to a three-variable system?

Back

A solution to a three-variable system is represented as an ordered triplet (x, y, z), indicating the values of the three variables.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

Infinitely many solutions occur when the equations represent the same plane or line in three-dimensional space, meaning they overlap completely.

Front

What is the elimination method used for?

Back

The elimination method is used to simplify a system of equations to find the values of the variables by eliminating one variable at a time.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the equations intersect at one or more points.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines or planes that do not intersect.

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How can you check the solution of a system of equations?

Back

You can check the solution by substituting the values back into the original equations to see if they hold true.