Special Cases when Solving a System of 3 Linear Equations

Special Cases when Solving a 3 Variable System of Equations Watch the video below to learn how to interpret a 3 variable system of equations that has infinite solutions or no solutions using the Desmos Matrix Calculator. Fill in the Blank - click the blank lines to choose the correct word that completes the sentences. If you solve a system with rref and see 0 0 0 0 in the last row, then this is a true statement and there are infinite solutions to the system. If you see 0 0 0 1 in the last row, then this is a false statement and the system has no solutions. Desmos Matrix Calculator Use this calculator to solve the problems below. 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 Solutions 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 Solutions What is the solution to the following system of equations? x + y + z = 2 2x + 2y + 2z = 4 - 3x - 3y - 3z = -6 (0, 0, 0) (1, 1, 2) Infinite Solutions No Solutions What is the solution to the following system of equations? x - y - 2z = 4 4x - 4y - z = 2 - x + y + 2z = -3 (1, -1, 0) (0, 0, 1) Infinite Solutions No Solutions What is the solution to the following system of equations? x + y + z = 13 x - z = -2 - 2x + y = 3 (2, -7, -4) (2, 7, 4) Infinite Solutions No Solutions