Basic 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 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 is the graphical representation of a system of equations?

Back

The graphs of the equations plotted on the same coordinate plane.

Front

What does it mean if two lines intersect at a point?

Back

The coordinates of the intersection point are the solution to the system of equations.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions, typically represented by parallel lines.

Front

What is a dependent system of equations?

Back

A system that has infinitely many solutions, represented by the same line.

Front

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

Back

The (x,y) coordinates must satisfy both equations.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What does it mean for two lines to be parallel?

Back

They have the same slope but different y-intercepts.

Front

What does it mean for two lines to be perpendicular?

Back

Their slopes are negative reciprocals of each other.