Solving Systems Using Elimination

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 eliminating one variable, allowing for the other variable to be solved directly.

Front

What is the first step in using elimination to solve the system: 2x + 2y = -2 and 3x - 2y = 12?

Back

Cross out the 2y and -2y.

Front

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

Back

It means that the lines represented by the equations are parallel and do not intersect.

Front

Solve the system: -12x - 10y = 0 and 6x + 5y = -1.

Back

No solution.

Front

What is the solution to the system: -4x - 2y = -12 and 4x + 8y = -24?

Back

(6, -6).

Front

What is the first step in using elimination for the system: 4x + 3y = 1 and x - 3y = -11?

Back

Cross out the 3y and -3y.

Front

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

Back

It indicates that the equations represent the same line, meaning every point on the line is a solution.

Front

Solve the system: 3x - 2y = 2 and 5x - 5y = 10.

Back

(-2, -4).

Front

What is the purpose of multiplying an equation in a system before using elimination?

Back

To create coefficients that are opposites, making it easier to eliminate one variable.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the lines intersect at one or more points.