SOLVING SYSTEMS OF EQUATIONS BY ELIMINATION

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 two lines are parallel in a system of equations?

Back

If two lines are parallel, they have the same slope and will never intersect, meaning there are no solutions to the system.

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines, which means they have the same slope but different y-intercepts.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

An infinite number of solutions occurs when the equations represent the same line, meaning every point on the line is a solution.

Front

Solve by elimination: 2x + 9y = -7 and 6x - 3y = 9.

Back

(1, -1)

Front

Solve using elimination: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7, -1)

Front

Solve using elimination: 7x + 2y = 24 and 8x + 2y = 30.

Back

(6, -9)

Front

Solve using elimination: -4x - 4y = 0 and 8x + 8y = 0.

Back

Infinite number of solutions.

Front

What is the first step in the elimination method?

Back

The first step is to align the equations so that corresponding variables and constants are in the same columns.

Front

What do you do if the coefficients of one variable are not the same?

Back

You can multiply one or both equations by a number to make the coefficients of one variable the same.