12/13/24 Classwork - Elimination Method

Front

What is the Elimination Method in solving systems of equations?

Back

The Elimination Method is a technique used to solve systems of linear equations by eliminating one variable, allowing for the solution of the remaining variable.

Front

How do you create a zero pair in the Elimination Method?

Back

To create a zero pair, you multiply one of the equations by a number that will make the coefficients of one of the variables opposites.

Front

What is the first step in using the Elimination Method?

Back

The first step is to align the equations and decide which variable to eliminate by making the coefficients of that variable opposites.

Front

Solve the system using elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

The system has no unique solution; it represents the same line.

Front

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

Back

It means the lines represented by the equations are parallel and will never intersect.

Front

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

Back

It means the equations represent the same line, and there are an infinite number of points that satisfy both equations.

Front

Solve the system using elimination: 3x + 2y = 12 and 6x + 4y = 24.

Back

The system has no unique solution; it represents the same line.

Front

What is the solution to the system: 5x - 3y = 7 and 2x + y = 4?

Back

(3, -1) is the solution.

Front

How do you check the solution of a system of equations?

Back

Substitute the solution back into both original equations to verify that both equations are satisfied.

Front

What is the significance of the coefficients in the elimination method?

Back

The coefficients determine how to manipulate the equations to eliminate a variable.