Systems of Equations: 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 removing one variable, making it easier to solve for the other.

Front

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

Back

By adding or subtracting the equations to cancel out one of the variables.

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 an infinite number of solutions, where the equations represent the same line.

Front

What is the first step in using the elimination method?

Back

Align the equations and decide which variable to eliminate.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinite number of solutions.

Front

Solve by elimination: 3x + 2y = 6 and 3x + 4y = 12.

Back

(0, 3).