Solving Systems Using 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 eliminating one variable 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 the first step in using elimination?

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?

Back

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

Front

What if the coefficients of one variable are opposites?

Back

You can add the equations directly to eliminate that variable.

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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