Systems of Equations: Choosing the Best Method

Front

What is a system of equations?

Back

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

Front

What does it mean if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

What is the substitution method?

Back

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

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 the equal values method?

Back

A method for solving systems of equations by setting the two equations equal to each other when both are solved for the same variable.

Front

When is the substitution method most effective?

Back

When one equation is already solved for one variable or can be easily manipulated to do so.

Front

When is the elimination method most effective?

Back

When the coefficients of one variable are the same or can be easily made the same.

Front

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

Back

Isolate one variable in one of the equations.