Systems of Equations

Front

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

Back

The graphs of the equations are parallel lines.

Front

What is the solution of a system of equations?

Back

An ordered pair that satisfies all equations in the system.

Front

How can you represent a system of equations graphically?

Back

By plotting the equations on a coordinate plane and finding the intersection point.

Front

What is the graphical representation of a consistent system of equations?

Back

The lines intersect at one point.

Front

What is the graphical representation of an inconsistent system of equations?

Back

The lines are parallel and do not 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.

Front

What is the definition of a dependent system of equations?

Back

A system where the equations represent the same line, resulting in infinitely many solutions.

Front

What is the purpose of using matrices in solving systems of equations?

Back

To organize and simplify the process of solving linear equations.

Front

What is a linear equation?

Back

An equation that forms a straight line when graphed, typically in the form y = mx + b.