Linear Programming WKST 9182021 4 07 PM 3

Linear Programming WKST 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 1

Linear Programming WKST 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 2

Linear Programming WKST 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 3

3 -Variable Systems Section 3. 4, © 2011, dangjim@gmail. com 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 4

Briefing of 3 -variable systems: Graphing in two dimensional x 9/18/2021 4: 07 PM + + + – – – + + + y – – – 3 -6: Three Variable Systems 5

Briefing of 3 -variable systems: + + + – – – + + + x 9/18/2021 4: 07 PM z + + + – – – y – Graphing in three dimensional 3 -6: Three Variable Systems 6

Video 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 7

Example 1 Solve: HINT: Look at the third equation (z = 3) and work backwards. 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 8

Example 1 Solve: z=3 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 9

Your Turn Solve: 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 10

Steps in 3 -variable systems A. Choose any two equations and eliminate one variable using elimination B. Choose two OTHER equations and eliminate the SAME variable using elimination C. With the two new equations, eliminate another variable D. Substitute the one variable in an equation in STEP 3 E. Substitute the two variables into any equation given F. Check the solution 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 11

Steps in 3 -step variables Steps: Eliminate Substitute in Step 3 Substitute in any equation Check 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 12

Example 2 Solve: 1. Choose any two equations and eliminate one variable using elimination Getting rid of x (1) + 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 13

Example 2 Solve: 2. Choose two OTHER equations and eliminate the SAME variable using elimination Getting rid of x (2) + 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 14

Example 2 Solve: 2. Choose two OTHER equations and eliminate the SAME variable using elimination (2) + 9/18/2021 4: 07 PM + 3 -6: Three Variable Systems 15

Example 2 Solve: 3. With the two new equations, eliminate another variable using elimination (– 1) + 9/18/2021 4: 07 PM + 3 -6: Three Variable Systems 16

Example 2 Solve: 4. Substitute to an equation in STEP 3 Doesn’t matter which equation to choose 9/18/2021 4: 07 PM + 3 -6: Three Variable Systems 17

Example 2 Solve: 5. Substitute the two variables into any equation given 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 18

Example 2 Solve: 6. Check the solution 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 19

Example 3 Solve: 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 20

Example 3 Solve: 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 21

Example 4 Solve: 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 22

Your Turn Solve: 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 23

Example 5 Solve: 9/18/2021 4: 07 PM 3 -6: Three Variable Systems 24

Example 6 Solve: 9/18/2021 4: 08 PM 3 -6: Three Variable Systems 25

Your Turn Solve: 9/18/2021 4: 08 PM 3 -6: Three Variable Systems 26

Assignment Worksheet 9/18/2021 4: 08 PM 3 -6: Three Variable Systems 27