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 any point on that 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 check your solution after solving a system of equations?

Back

You can check your solution by substituting the values back into the original equations to see if they hold true.

Front

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

Back

The coefficients determine the slope and position of the lines represented by the equations, affecting the number of solutions.

Front

What is a consistent system of equations?

Back

A consistent system has at least one solution, which can be either a unique solution or infinitely many solutions.

Front

What is an inconsistent system of equations?

Back

An inconsistent system has no solutions, typically represented by parallel lines.

Front

How do 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 graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane to visualize their intersection points, which represent the solutions.