Solving Systems of Equations

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 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

When is the substitution method preferred?

Back

When one equation is easily solvable for one variable.

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 determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution; an inconsistent system has no solutions.

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations.

Front

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

Back

Isolate one variable in one of the equations.