Solve Systems of 3 Linear Equations using SUBSTITUTION METHOD (Part 2)

Master solving 3-variable linear systems using substitution!

Types of Solutions of Systems of 3 Linear Equations A system of 3 linear equations can have one solution, no solution, or infinite solutions. Special Cases when Solving a System of 3 Linear Equations Watch the video and then answer the questions below. If you get rid of all the variables and run into a true numerical state (an identity such as 0 = 0), you have run into a dependent system which has _ solution(s)? Infinite If you get rid of all the variables and run into a false numerical statement (such as 0=2), you have run into an inconsistent system and there is _ solutions(?) No If you do not eliminate all the variables, you have a consistent and dependent system with _ solution(s)? 1 What is the solution to the following system of equations? 2 x + y - 3 z = 0 4x + 2y - 6z = 0 x - y + z = 0 (1, 2, 1) (0, 0, 0) Infinite Solutions No Solution What is the solution to the following system of equations? x + y + z = 2 x - y + 3z = 4 2x + 2y + z = 3 (0, 1, 1) (1, 0, 1) Infinite Solutions No Solution What is the solution to the following system of equations? x - y +3 z = 0 2x - 2y + 6z = 6 4x + 2y - 6z = 0 (1, 2, 1) (0, 0, 0) Infinite Solutions No Solution Solve the system of equations using the Substitution Method.Click the blank to enter the solution for the values of x, y, and z. ( 1, 2, 1)