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

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

Back

A system has no solution when the equations represent parallel lines that never intersect.

Front

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

Back

A system has infinitely many solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

Solve using elimination: 4x - 2y = 16 and 5x + 2y = 11.

Back

(3, -2)

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: 10x - 8y = -30 and -10x + 9y = 25. Which variable will be eliminated?

Back

the x

Front

What is the solution to the system: 7x + 1y = -9 and -3x - 1y = 5?

Back

(-1, -2)

Front

What is the significance of coefficients in elimination?

Back

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

Front

Solve using elimination: -2x + 2y = 0 and 2x + 6y = -16.

Back

(-2, -2)

Front

What is a key advantage of the elimination method?

Back

It can be more straightforward than substitution, especially when dealing with complex equations.