Solving Systems Using Elimination

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves combining two equations to eliminate one variable, making it easier to solve for the other variable.

Front

What does it mean to 'eliminate' a variable in a system of equations?

Back

To 'eliminate' a variable means to combine equations in such a way that one of the variables cancels out, allowing for the other variable to be solved.

Front

If you have the equations 2x + 3y = 6 and 4x + 6y = 12, can you eliminate a variable?

Back

Yes, you can eliminate a variable because the second equation is a multiple of the first.

Front

What is the first step in using 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 combine them.

Front

What do you do if the coefficients of the variables are opposites?

Back

If the coefficients are opposites, you can add the equations directly to eliminate that variable.

Front

What is the solution to the system of equations 3x + 4y = 10 and 3x - 2y = 4?

Back

The solution is (2, 1).

Front

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

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What is the significance of the coefficients in the elimination method?

Back

Coefficients determine how the equations can be combined; they must be manipulated to create opposites for elimination.

Front

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

Back

You can substitute the solution back into the original equations to see if both equations are satisfied.

Front

What is a consistent system of equations?

Back

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