Solving Systems 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

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

Back

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

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, so every point on the line is a solution to the system.

Front

What is the first step in using the elimination method?

Back

The first step is to align the equations and manipulate them (if necessary) so that when added or subtracted, one variable will cancel out.

Front

How can you manipulate equations to use the elimination method?

Back

You can multiply one or both equations by a constant to create coefficients that will allow for elimination of a variable.

Front

What is the solution to the system of equations -4x - 2y = -12 and 4x + 8y = -24?

Back

The solution is (6, -6).

Front

What does it indicate if the elimination method results in a true statement like 0 = 0?

Back

It indicates that the system has infinitely many solutions.

Front

What is the solution to the system of equations 3x + 7y = 23 and -3x - 7y = -17?

Back

The system has no solution.

Front

How do you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

What is the solution to the system of equations 7x + y = -9 and -3x - y = 5?

Back

The solution is (-1, -2).