SOE Elimination

Front

What is the elimination method in solving systems of equations?

Back

The elimination method is a technique used to solve systems of linear equations by eliminating one variable, allowing for the solution of the remaining variable.

Front

What does it mean if a system of equations has no solutions?

Back

It means that the lines represented by the equations are parallel and do not intersect.

Front

What is an ordered pair in the context of solving equations?

Back

An ordered pair is a pair of numbers (x, y) that represents the solution to a system of equations, where x is the value of the first variable and y is the value of the second variable.

Front

How do you determine which variable to eliminate when using the elimination method?

Back

You can determine which variable to eliminate by looking for coefficients that are opposites or can be made opposites through multiplication.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations so that like terms are in the same column, making it easier to eliminate a variable.

Front

If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude about the system?

Back

The system has infinite solutions because the second equation is a multiple of the first, meaning they represent the same line.

Front

What happens if you add two equations together in the elimination method?

Back

If you add two equations together, you can eliminate one of the variables if their coefficients are opposites.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting whether they intersect, are parallel, or are the same line.

Front

How can you check your solution after using the elimination method?

Back

You can check your solution by substituting the ordered pair back into the original equations to see if both equations are satisfied.

Front

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

Back

It means that the equations represent the same line, and there are countless points (ordered pairs) that satisfy both equations.