Systems of Linear Equations and Inequalities Review

Front

What is a system of linear equations?

Back

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

Front

What does it mean for a system to be consistent?

Back

A consistent system has at least one solution.

Front

What does it mean for a system to be inconsistent?

Back

An inconsistent system has no solutions.

Front

What does it mean for a system to be dependent?

Back

A dependent system has infinitely many solutions.

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

How do you classify a system with one solution?

Back

It is classified as consistent and independent.

Front

How do you classify a system with no solutions?

Back

It is classified as inconsistent.

Front

How do you classify a system with infinitely many solutions?

Back

It is classified as consistent and dependent.

Front

What is the graphical representation of a linear inequality?

Back

A shaded region on one side of the boundary line, indicating all the solutions to the inequality.