Solving Systems Using Elimination Warm Up

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 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

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

Back

( -3 , 4 )

Front

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

Back

( 6 , -6 )

Front

Solve the system: 2m + 3n = 6 and -m + 2n = 5.

Back

( -1, 2 )

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

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 equations represent parallel lines.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations.

Front

How do you determine if two equations are dependent?

Back

Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.