Solving 3-variable systems REVIEW

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by removing one variable, allowing for easier solving of the remaining equations.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equations.

Front

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

Back

The equations represent the same line or plane, meaning there are countless points that satisfy all equations.

Front

What does it mean if a system has no solution?

Back

The equations represent parallel lines or planes that never intersect.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution values back into the original equations to see if they hold true.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.

Front

What is a dependent system of equations?

Back

A system where the equations are equivalent, leading to infinitely many solutions.