Solving Systems - Elimination Method (GREEN)

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 the elimination method?

Back

The first step is to manipulate the equations so that when added or subtracted, one of the variables cancels out.

Front

Solve by elimination: 4x + 3y = 1 and x - 3y = -11.

Back

(7,0)

Front

Solve by elimination: -6x + 5y = 1 and 6x + 4y = -10.

Back

(-1,-1)

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 never intersect.

Front

Solve by elimination: 7x + y = -9 and -3x - y = 5.

Back

(-1,-2)

Front

What is the significance of the coefficients in the elimination method?

Back

The coefficients determine how to manipulate the equations to eliminate a variable.

Front

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

Back

No Solution

Front

What is a consistent system of equations?

Back

A consistent system 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 has no solutions, meaning the lines are parallel.