Solving Systems with Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system using elimination?

Back

Elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the first step in solving a system of equations by elimination?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

How do you eliminate a variable in a system of equations?

Back

Multiply one or both equations by a number so that when added or subtracted, one variable cancels out.

Front

What is the solution to a system of equations?

Back

The point (x, y) where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

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

Back

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

Front

How can you check if your solution to a system of equations is correct?

Back

Substitute the values of the variables back into the original equations to see if they hold true.

Front

What is the combined equation for the system: 2x + 3y = 6 and 4x + 6y = 12?

Back

The combined equation is 0 = 0, indicating infinitely many solutions.

Front

What is the elimination method used for?

Back

To find the values of variables in a system of equations by eliminating one variable.