Systems of Equations in Three Variables

Front

________________ is a set of two or more equations that have the same variables.

Back

system of equations

Front

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

Back

(1, -3, -2)

Front

Solve the system: x + 2y + 3z = 6, 2x - y + z = 4, -x + 3y - 2z = -1

Back

(-1, 6, 1)

Front

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

Back

(2, -2, 3)

Front

Solve the system: x + y + z = 0, 2x - y + 3z = 1, -x + 4y - z = 2

Back

None of these

Front

What is the elimination method?

Back

A method for solving systems of equations by eliminating one variable at a time.

Front

What is a solution of a system of equations?

Back

A set of values for the variables that makes all equations true.

Front

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

Back

The equations represent parallel lines or planes that do not intersect.

Front

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

Back

It is represented as the intersection of three planes in three-dimensional space.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equations.