Solving Systems

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 has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system has one solution?

Back

The lines intersect at exactly one point.

Front

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

Back

The lines are the same, meaning they overlap completely.

Front

What is the elimination method?

Back

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

Front

What is the substitution method?

Back

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

Front

How can you determine if a system has no solution?

Back

If the equations represent parallel lines with the same slope but different y-intercepts.

Front

How can you determine if a system has infinitely many solutions?

Back

If the equations represent the same line, meaning they have the same slope and y-intercept.

Front

What is the graphical representation of a system of equations?

Back

The points where the lines intersect represent the solutions to the system.

Front

What is a consistent system?

Back

A system of equations that has at least one solution.