3B - Solving Linear Systems in Three Variables

Front

What is a linear system in three variables?

Back

A linear system in three variables consists of three linear equations with three unknowns (x, y, z) that can be solved simultaneously.

Front

What is the solution of a system of three linear equations called?

Back

Ordered Triple

Front

How do you determine if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel planes that do not intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same plane or are dependent, leading to an infinite number of intersection points.

Front

Solve the system: 2x + y - z = 3, x - y + 2z = 1, 3x + 2y + z = 10.

Back

(2, -1, 1)

Front

What is the graphical representation of a solution to a system of three equations?

Back

The solution is represented by the point of intersection of three planes in three-dimensional space.

Front

What is an ordered triple?

Back

An ordered triple is a set of three numbers (x, y, z) that represent a point in three-dimensional space.

Front

How can you check if a solution is correct for a system of equations?

Back

Substitute the values of the solution into each equation to see if they hold true.

Front

Solve the system: x + 2y + 3z = 1, 2x - y + z = 3, 3x + y - z = 0.

Back

(1, 0, 0)

Front

What is the elimination method in solving linear systems?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the others.