Systems of Three Variables

Front

What is the solution to a 3-variable system of equations?

Back

The intersection of three planes.

Front

What does it mean if you are left with 0 = 17 after eliminating variables?

Back

No solution.

Front

Is (4,5,6) a solution to the equation 2x - 3y + z = 8?

Back

No.

Front

What is the term for the solution of a system of three linear equations in three variables (x, y, z)?

Back

Ordered Triple.

Front

In the system of equations, which variable should be eliminated first: 2x - 3y - z = 33, 5x + 2y + z = 1, 3x + 4y - z = -5?

Back

z.

Front

What is a system of equations?

Back

A set of equations with the same variables.

Front

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

Back

The equations represent the same plane or line.

Front

What is the graphical representation of a system of three variables?

Back

Three-dimensional space with planes.

Front

What is the significance of the intersection point in a system of three equations?

Back

It represents the unique solution to the system.

Front

What happens if two planes in a three-variable system are parallel?

Back

They do not intersect, leading to no solution.