 SOLVE SYSTEMS OF LINEAR EQUATIONS IN THREE VARIABLES.  USE SYSTEMS OF THREE EQUATIONS TO SOLVE APPLIED PROBLEMS.  MODEL A SITUATION USING A QUADRATIC FUNCTION. Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley 9.2 Systems of Equations in Three Variables

Solving Systems of Equations in Three Variables Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley A linear equation in three variables is an equation equivalent to one of the form Ax + By + Cz = D. A, B, C, and D are real numbers and A, B, and C are not 0. A solution of a system of three equations in three variables is an ordered triple that makes all three equations true. Example: The triple (4, 0,  3) is the solution of this system of equations. We can verify this by substituting 4 for x, 0 for y, and  3 for z in each equation. x  2y + 4z =  8 2x + 2y  z = 11 x + y  2z = 10

Example Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley Solve the system x + 3y + 2z = 9 x  y + 3z = 16 3x  4y + 2z = 28

Practice Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley

Application Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley A food service distributor conducted a study to predict fuel usage for new delivery routes, for a particular truck. Use the chart to find the rates of fuel in rush hour traffic, city traffic, and on the highway Highway Hours 34186Week Week Week 1 Total Fuel Used (gal) City Traffic Hours Rush Hour Hours