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 if two lines intersect on a graph?

Back

The system of equations has one unique solution.

Front

What does it mean if two lines are parallel on a graph?

Back

The system of equations has no solution.

Front

What does it mean if two lines coincide on a graph?

Back

The system of equations has infinitely many solutions.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations; if it satisfies both, it is a solution.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and then 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.

Front

What is the graphical method for solving systems of equations?

Back

Plotting both equations on a graph and identifying their intersection point.

Front

What does it mean for a system of equations to be consistent?

Back

The system has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

The system has no solutions.