KP Dec 3 3B - Solving Linear Systems in Three Variables

Front

Solve the system of equations: 2x + 3y + z = 1, x - y + 2z = 3, 3x + y - z = 2

Back

(1, -1, 2)

Front

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

Back

Ordered Triple

Front

Solve the system of equations: x + 2y + 3z = 6, 2x - y + z = 4, 3x + 3y + z = 10

Back

(2, 0, 0)

Front

What does it mean if a system of equations has no solution?

Back

The lines represented by the equations are parallel and do not intersect.

Front

Solve the system of equations: 4x + y - z = 5, x - 2y + 3z = 4, 2x + y + z = 3

Back

(1, 1, 1)

Front

What is an ordered triple?

Back

A solution to a system of three equations in three variables, represented as (x, y, z).

Front

Solve the system of equations: 5x - 2y + z = 3, 3x + 4y - z = 7, 2x - y + 3z = 1

Back

(1, 1, 0)

Front

What is the graphical representation of a system of three linear equations?

Back

It can be represented as three planes in three-dimensional space.

Front

Solve the system of equations: x + y + z = 6, 2x + 2y + z = 8, x - y + z = 2

Back

(2, 2, 2)

Front

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

Back

The equations represent the same plane or lines that coincide.