Solving Systems of Equations by Elimination (Makeup)

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 the other variable to be solved directly.

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the equations represent parallel lines that never intersect.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

Why is it important to line up like terms when using the Elimination Method?

Back

Lining up like terms ensures that the coefficients of the variables are aligned, making it easier to eliminate one variable.

Front

What is a consistent system of equations?

Back

A consistent system of equations is one that has at least one solution, which can be either a unique solution or infinitely many solutions.

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations is one that has no solutions, typically represented by parallel lines.

Front

What is the first step in the Elimination Method?

Back

The first step is to manipulate the equations (if necessary) so that the coefficients of one of the variables are opposites.

Front

How can you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations are equivalent, meaning they represent the same line.

Front

What is the role of coefficients in the Elimination Method?

Back

Coefficients are the numerical factors in front of the variables, and they are manipulated to eliminate one variable during the solving process.

Front

What does it mean for two equations to be dependent?

Back

Two equations are dependent if they represent the same line, leading to infinitely many solutions.