Solving Systems Using Elimination Warm Up

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

What is the first step in using elimination to solve the system: 4x + 3y = 1 and x - 3y = -11?

Back

Cross out the 3y and -3y.

Front

What is the first step in using elimination to solve the system: 2x + 2y = -2 and 3x - 2y = 12?

Back

Cross out the 2y and -2y.

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 do not intersect.

Front

Solve the system: -4x - 2y = -12 and 4x + 8y = -24.

Back

(6, -6)

Front

Solve the system: 2x + 3y = 6 and x + 2y = 5.

Back

(-3, 4)

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 every point on that line is a solution.

Front

Solve the system: 3x - 2y = 2 and 5x - 5y = 10.

Back

(-2, -4)

Front

What is the purpose of changing the signs of an equation in elimination?

Back

Changing the signs can help to align coefficients of one variable to facilitate elimination.

Front

What is a key indicator that a system of equations can be solved using elimination?

Back

The coefficients of one variable in both equations can be made equal or opposites.