Solving Systems by Elimination

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 adding or subtracting equations to eliminate a variable.

Front

How do you eliminate a variable in a system of equations?

Back

By manipulating the equations (adding or subtracting) so that one variable cancels out.

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 that has infinitely many solutions, where the equations represent the same line.

Front

What is the first step in the elimination method?

Back

Align the equations so that corresponding variables are in the same column.

Front

If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude?

Back

The system is dependent; both equations represent the same line.

Front

What is the solution to the system: 2x + 3y = 6 and x - y = -1?

Back

(2, -3) is the solution.