Intermediate Algebra chapter 4

Third-Order Systems of Linear Equations Chapter 4

General Ideas "Third-Order Systems of Linear Equations" is just a fancy way of saying 3 equations in 3 unknowns, or 3 equations in 3 variables. An example of a system of 3 equations in 3 unknowns: 3x + 7y - z = 6 (1) 2x - 3y + 2z = 7 (2) -2x - 2y + 3z = 8 (3) The 3 unknows are x, y, and z. A solution will be an ordered triple (x, y, z). Observe that for the above example: (1, 1, 4) satifies all 3 equations. Plug x = 1, y = 1, and z = 4 into equations (1), (2), and (3), and all equations hold true. (0, 0, 1) does not satisfy any of the 3 equations, so it can't be the solution. Plug x = 0, y = 0, and z = 1 into equations (1), (2), and (3), and none of the equations are true. Conclusion: (1, 1, 4) is a solution to the example system of equations. (0, 0, 1) is not a solution to the example system of equations.