Systems by Elimination PART 1

Front

What is the elimination method in solving systems of equations?

Back

The elimination method is a technique used to solve systems of equations by adding or subtracting the equations to eliminate one of the variables.

Front

What happens when you add two equations in a system where the coefficients of x are the same?

Back

The x's will be eliminated.

Front

What happens when you add two equations in a system where the coefficients of y are the same?

Back

The y's will be eliminated.

Front

What does it mean if both variables are eliminated when adding two equations?

Back

It indicates that the equations are dependent and represent the same line, leading to an infinite number of solutions.

Front

What does it mean if none of the variables are eliminated when adding two equations?

Back

It means that the equations are independent and will intersect at a single point, providing a unique solution.

Front

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

Back

Infinite number of solutions.

Front

Solve the system by elimination: 3x - 2y = 5 and 6x - 4y = 10.

Back

Infinite number of solutions.

Front

Solve the system by elimination: 4x - 6y = -6 and -2x - 12y = -12.

Back

(0, 1).

Front

What is a unique solution in the context of systems of equations?

Back

A unique solution occurs when the two equations intersect at exactly one point, providing specific values for both variables.

Front

What is an infinite number of solutions in the context of systems of equations?

Back

An infinite number of solutions occurs when the two equations represent the same line, meaning every point on the line is a solution.