System of Equations Flashcard Review

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What does it mean for a system of equations to have no solution?

Back

It means that there are no values for the variables that can satisfy all equations in the system, often because the lines are parallel.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that there are countless sets of values for the variables that satisfy all equations, often because the equations represent the same line.

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What is the slope-intercept form of a linear equation?

Back

Front

What is the graphical representation of a system of equations?

Back

The graphical representation is the intersection points of the lines representing the equations.

Front

How do you find the solution to a system of equations graphically?

Back

You find the point where the lines intersect on the graph.

Front

What is the significance of the y-intercept in a linear equation?

Back

Front

What is the difference between intersecting lines and parallel lines?

Back

Intersecting lines cross at one point, while parallel lines never meet.