Flashcard Solving 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 for 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 add or subtract the equations in such a way that one of the variables cancels out.

Front

What is the first step in using the elimination method?

Back

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

Front

Solve the system using elimination: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7, -1)

Front

What does it mean for a system of equations to be consistent?

Back

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

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system has no solutions, meaning the lines represented by the equations are parallel and never intersect.

Front

What is a dependent system of equations?

Back

A dependent system has infinitely many solutions, meaning the equations represent the same line.

Front

Solve the system using elimination: 4x + 4y = 4 and 3x + 4y = 10.

Back

x = -6, y = 7

Front

What is the preferred method for solving systems of equations when coefficients are easy to manipulate?

Back

The elimination method is often preferred when coefficients can be easily manipulated to eliminate a variable.

Front

Solve the system: y = -1x - 5 and 4x - 8y = 4.

Back

(-3, -2)