Lesson 17-5: Classifying Systems of Equations (12/9)

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 one solution?

Back

The lines representing the equations intersect at exactly one point.

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 lines representing the equations coincide, meaning they are the same line.

Front

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

Back

Substitute the point into each equation; if it satisfies all equations, it is a solution.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, which is then substituted into the other equation.

Front

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) of intersection.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.

Front

How do you identify a consistent system of equations?

Back

A system that has at least one solution (either one or infinitely many solutions).