Solving Systems With 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

What is a system of equations?

Back

A system of equations is a set of two or more equations that have the same variables.

Front

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

Back

(0, 1)

Front

Solve by elimination: 5x + y = 9 and 10x - 7y = -18.

Back

(1, 4)

Front

Solve by elimination: -x - 7y = 14 and -4x - 14y = 28.

Back

(0, -2)

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions.

Front

What is the first step in the elimination method?

Back

The first step is to manipulate the equations to align coefficients of one variable for elimination.

Front

Solve by elimination: 8x + 14y = 4 and -6x - 7y = -10.

Back

(4, -2)

Front

What is the purpose of multiplying an equation in the elimination method?

Back

Multiplying an equation allows you to create equivalent equations that can be added or subtracted to eliminate a variable.