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

Front

What does it mean to eliminate a variable?

Back

To eliminate a variable means to manipulate the equations in such a way that one variable is removed, making it possible to solve for the other variable.

Front

In the system 4x + 8y = 20 and -4x + 2y = -30, which variable will be eliminated?

Back

The variable x will be eliminated.

Front

Solve by elimination: 4x - 6y = -6 and -2x - 12y = -12. What is the solution?

Back

The solution is (0, 1).

Front

Solve by elimination: 2x + 9y = -7 and 6x - 3y = 9. What is the solution?

Back

The solution is (1, -1).

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28. What is the solution?

Back

The solution is (7, 0).

Front

Solve by elimination: 7x + y = -9 and -3x - y = 5. What is the solution?

Back

The solution is (-1, -2).

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

What do you do if the coefficients of the variable you want to eliminate are not the same?

Back

You can multiply one or both equations by a number to make the coefficients of the variable the same.