Solve 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 elimination in the context of solving systems of equations?

Back

A method to eliminate one variable by adding or subtracting equations.

Front

What is the first step in the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

What do you do if the coefficients of one variable are the same in both equations?

Back

You can subtract one equation from the other to eliminate that variable.

Front

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

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

Front

What is an ordered pair in the context of systems of equations?

Back

A pair of numbers (x, y) that represents the solution to the system.

Front

What is the significance of the point (0,0) in systems of equations?

Back

It is the origin and can be a solution if it satisfies the equations.