Understanding Systems of Linear Equations in Three Variables

What does the graph of a linear equation in two variables form?

• A curve

• A point

• A line

• A plane

How can a system of three linear equations in three variables be represented?

• As three intersecting lines

• As a single plane

• As a group of three planes

• As a cube

What type of solution exists when two lines in a system are distinct and parallel?

• No solutions

• A circular solution

• An infinite number of solutions

• A single unique solution

What happens when all three planes in a system intersect at a single point?

• The system has no solutions

• The system has a single unique solution

• The system has an infinite number of solutions

• The system forms a cube

What is the result when two planes in a system are parallel and distinct?

• The system has no solutions

• The system has a single unique solution

• The system forms a triangle

• The system has an infinite number of solutions

When do systems of three variables have an infinite number of solutions?

• When all three planes coincide or intersect along a line

• When two planes are distinct and parallel

• When all three planes are parallel

• When the planes form a cube

What is the result when three planes intersect along three distinct parallel lines?

• The system forms a cube

• The system has an infinite number of solutions

• The system has no solutions

• The system has a single unique solution

What is a system called if it has one or more solutions?

• Dependent

• Independent

• Inconsistent

• Consistent

What term describes equations with identical graphs?

• Consistent

• Inconsistent

• Dependent

• Independent

What is the term for a system with no solutions?

• Consistent

• Dependent

• Independent

• Inconsistent