Systems of Equations Substitution and Elimination Methods

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, allowing for the other to be solved.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

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

The equations represent the same line, meaning every point on the line is a solution.

Front

How do 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 the elimination method?

Back

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

Front

What is the first step in the substitution method?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.