System 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 adding or subtracting equations to eliminate a variable.

Front

What is the first step in the elimination method?

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

Adjust the equations (by multiplying if necessary) so that when added or subtracted, one variable cancels out.

Front

What does it mean if two equations represent the same line?

Back

They have infinitely many solutions because every point on the line is a solution.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

What does it mean if two lines intersect at one point?

Back

The system has one unique solution.

Front

What happens if two lines are parallel?

Back

The system has no solution because the lines never intersect.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.