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

Front

How can you determine the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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.

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into the original equations to see if they hold true.