System of Equations Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

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

Back

It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

Front

What is the elimination method?

Back

A method for solving systems of equations by eliminating one variable, making it easier to solve for the other.

Front

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

Back

It means that the equations represent the same line, and there are countless points (x,y) that satisfy both equations.

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect, so there are no points (x,y) that satisfy both.

Front

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

Back

Infinite solutions.

Front

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

Back

Infinite solutions.

Front

Solve by elimination: x + y = 5 and x - y = 1.

Back

(3,2).

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.