Solve systems by 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 the other variable to be solved directly.

Front

How do you eliminate a variable in a system of equations?

Back

To eliminate a variable, you can multiply one or both equations by a number so that the coefficients of one of the variables are opposites, allowing you to add or subtract the equations.

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.

Front

What do you do after eliminating a variable in a system of equations?

Back

After eliminating a variable, solve the resulting equation for the remaining variable.

Front

How do you find the value of the eliminated variable after solving for the other variable?

Back

Substitute the value of the solved variable back into one of the original equations to find the value of the eliminated variable.

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

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

Front

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

Back

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

Front

What is the significance of the coefficients in a system of equations when using elimination?

Back

The coefficients determine how to manipulate the equations to eliminate a variable; they must be adjusted to create opposites.

Front

Can the elimination method be used for non-linear systems?

Back

The elimination method is primarily used for linear systems, but it can be adapted for some non-linear systems with appropriate modifications.