Solving Systems of Linear Equations in Three Variables

Front

What is a system of linear equations?

Back

A set of two or more linear equations in the same variables.

Front

What does the graph of a system of equations with no solution look like?

Back

Parallel lines.

Front

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

Back

Ordered Triple (x, y, z).

Front

How many solutions can a system of linear equations have?

Back

A system can have one solution, no solution, or infinitely many solutions.

Front

What is the method used to solve systems of equations by substitution?

Back

Solve one equation for one variable and substitute that expression into the other equations.

Front

What is the elimination method in solving systems of equations?

Back

Adding or subtracting equations to eliminate one variable, making it easier to solve for the others.

Front

What does it mean if two equations are dependent?

Back

They represent the same line and have infinitely many solutions.

Front

What does it mean if two equations are independent?

Back

They represent different lines and have exactly one solution.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The lines coincide (overlap completely).

Front

What is the first step in solving a system of equations using the substitution method?

Back

Isolate one variable in one of the equations.