Systems of Equations Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by eliminating one variable, making it easier to solve for the other.

Front

How do you use multiplication in the elimination method?

Back

Multiply one or both equations by a number to align coefficients for elimination.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have no solutions because they never intersect.

Front

What does it mean if two lines are coincident in a system of equations?

Back

They have infinitely many solutions because they lie on top of each other.

Front

What is a unique solution in a system of equations?

Back

A single point where the two lines intersect, representing one solution for the variables.

Front

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

Back

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

Front

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

Back

Align the equations so that corresponding variables are in the same position.

Front

What is the result of the elimination method if the equations are dependent?

Back

The result will be a true statement, indicating infinitely many solutions.