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 equations by eliminating one variable, allowing for the other variable to be solved directly.

Front

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

Back

To eliminate a variable, you can multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing you to add or subtract the equations.

Front

Solve by elimination: 2x + 3y = 6 and 4x - 3y = 12.

Back

(3, 0)

Front

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

Back

A system of equations has no solution if the lines represented by the equations are parallel and never intersect.

Front

Solve by elimination: 3x + 4y = 10 and 6x + 8y = 20.

Back

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

Front

What is a consistent system of equations?

Back

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

Front

What is an inconsistent system of equations?

Back

An inconsistent system of equations is one that has no solutions, meaning the lines are parallel.

Front

Solve by elimination: x + 2y = 8 and 3x + 2y = 14.

Back

(4, 0)

Front

What is the first step in using the elimination method?

Back

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

Front

Solve by elimination: 5x - 2y = 3 and 3x + 2y = 11.

Back

(3, 6)