Solve Systems with 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 equations by eliminating one variable, allowing for the other variable to be solved directly.

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables.

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

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

Back

It means that the equations represent the same line, and thus every point on the line is a solution.

Front

How do you determine if a system of equations has a unique solution?

Back

A system has a unique solution if the lines represented by the equations intersect at exactly one point.

Front

What is the first step in using the elimination method?

Back

The first step is to manipulate the equations to align coefficients of one variable for elimination.

Front

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

Back

(3, 0) is the solution.

Front

Solve the system: 5x - 2y = 10 and 3x + 4y = 24.

Back

(4, 2) is the solution.

Front

What is the purpose of multiplying an equation in the elimination method?

Back

To create equivalent equations that allow for the elimination of one variable.

Front

Solve by elimination: 3x + 2y = 12 and 6x + 4y = 24.

Back

Infinitely many solutions.