Systems of Equations 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 eliminate a variable in a system of equations?

Back

To manipulate the equations so that one variable cancels out, allowing for the solution of the other variable.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is a zero pair in the context of elimination?

Back

A pair of terms that add up to zero, allowing for the cancellation of a variable.

Front

How do you create a zero pair?

Back

By multiplying one of the equations by a number that will make the coefficients of one variable opposites.

Front

What is the first step in using the elimination method?

Back

Align the equations and decide which variable to eliminate.

Front

What does it mean to multiply an equation by -1?

Back

It changes the signs of all terms in the equation, effectively flipping the equation.

Front

What is the solution to a system of equations?

Back

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

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.