Systems-Elimination Flashcard

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

Front

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

Back

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

Front

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

Back

Infinitely many solutions.

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 using elimination: 3x - 2y = 5 and 6x - 4y = 10.

Back

Infinitely many solutions.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either one solution or infinitely many solutions.

Front

Solve using elimination: x + y = 2 and x - y = 0.

Back

(1, 1).

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, meaning the lines represented by the equations do not intersect.

Front

Solve using elimination: 5x + 3y = 15 and 10x + 6y = 30.

Back

Infinitely many solutions.