Elimination method

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 other variable to be solved directly.

Front

How do you eliminate a variable in the Elimination Method?

Back

To eliminate a variable, you can add or subtract the equations in such a way that one variable 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 using the Elimination Method: 2x + 3y = 6 and 4x + 6y = 12.

Back

No solution (the second equation is a multiple of the first, indicating they represent the same line).

Front

Solve using the Elimination Method: x + y = 10 and x - y = 2.

Back

(6, 4) - x = 6, y = 4.

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 will never intersect.

Front

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

Back

It means that the equations represent the same line, and thus every point on the line is a solution.

Front

Solve using the Elimination Method: 3x + 2y = 12 and 6x + 4y = 24.

Back

No solution (the second equation is a multiple of the first).

Front

Solve using the Elimination Method: 5x - 2y = 3 and 3x + 2y = 15.

Back

(3, 0).

Front

What is the significance of the coefficients in the Elimination Method?

Back

The coefficients determine how the equations can be manipulated to eliminate a variable.