Section 3.6 Systems of Linear Equations in Three Variables and Applications 285 Solving a System of Linear Equations in Three Variables A B A C Step 2: Eliminate the y variable from equations and . 4x 2y 6z 14 3x 2y z 1 1 7x 5z 3 2x y 3z 7 3x 2y z 11 A B A B Multiply by 2. Multiply by 3. Multiply by 4. E D Multiply by 7. Solve the system. Solution: 2x y 3z 7 3x 2y z 11 2x 3y 2z 3 A B C 2x y 3z 7 3x 2y z 11 2x 3y 2z 3 Example 1 Step 1: The equations are already in standard form. • It is often helpful to label the equations. • The y variable can be easily eliminated from equations and and from equations and . This is accomplished by creating opposite coefficients for the y terms and then adding the equations. TIP: It is important to note that in steps 2 and 3, the same variable is eliminated. Step 3: Eliminate the y variable again, this time from equations and . Step 4: Now equations and can be paired up to form a linear system in two variables. Solve this system. 28x 20z 12 28x 77z 126 57z 114 z 2 Once one variable has been found, substitute this value into either equation in the two-variable system, that is, either equation or . Substitute z 2 into equation D . 7x 5z 3 7x 5122 3 7x 10 3 7x 7 x 1 D D E 7x 5z 3 4x 11z 18 D E D E 6x 3y 9z 21 2x 3y 2z 3 4x 11z 18 2x y 3z 7 2x 3y 2z 3 A C A C
miller_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above