Solving Systems - Elimination Method (GREEN)

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 the first step in using the elimination method?

Back

The first step is to manipulate the equations to align coefficients of one variable so that they can be eliminated when the equations are added or subtracted.

Front

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

Back

You can eliminate a variable by adding or subtracting the equations after adjusting their coefficients to be equal.

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 every point on the line is a solution.

Front

How can you check if your solution to a system of equations is correct?

Back

You can check the solution by substituting the values back into the original equations to see if they hold true.

Front

What is the solution to the system: 2x + 3y = 6 and 4x + 6y = 12?

Back

The solution is infinitely many solutions, as the second equation is a multiple of the first.

Front

What is the solution to the system: 3x + 2y = 12 and 3x + 2y = 6?

Back

The system has no solution, as the equations represent parallel lines.

Front

How do you prepare equations for elimination?

Back

You may need to multiply one or both equations by a constant to align the coefficients of one variable.

Front

What is the result of adding the equations 2x + 3y = 6 and -2x + y = 4?

Back

The result is 4y = 10, which simplifies to y = 2.5.