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, and thus 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 the coefficients of one variable are opposites.

Front

How can you manipulate equations to prepare for elimination?

Back

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

Front

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

Back

The coefficients determine how the equations can be combined to eliminate a variable.

Front

What should you do if the coefficients of the variable you want to eliminate are already opposites?

Back

You can directly add or subtract the equations to eliminate that variable.

Front

What is the result of adding two equations in a system?

Back

The result is a new equation that combines the information from both original equations, potentially simplifying the system.

Front

How do you check your solution after solving a system of equations?

Back

Substitute the solution back into the original equations to verify that both equations are satisfied.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, meaning the lines intersect at one point or are the same line.