Solving 3 Variable Systems St Augustine Preparatory School
Solving 3 -Variable Systems St. Augustine Preparatory School October 7, 2016
Solving Equations with Missing Variables The following system has 3 different variables within the system, but each equation is missing one of the three. 6 x – 12 y = -5 (missing z) 8 y + z = 0 (missing x) 9 x – z = 12 (missing y) In this situation you must be careful about which variables you cancel using elimination.
1. Use two of the equations to cancel out the same variable that is missing from the third. 2. Use the resulting equation from step one and the third equation to cancel out one more variable. 3. Use the variable you found in step 2, along with one of the equations from step 2 to calculate a second variable. 4. Use one of the original equations to calculate the final variable.
Example Solution: 6 x – 12 y = -5 8 y + z = 0 9 x – z = 12 Step 1: 6 x – 12 y = -5 (x 2) 8 y + z = 0 (x 3) Step 2: 12 x + 3 z = -10 9 x - z = 12 (x 3) 12 x – 24 y = -10 8 y + 3 z = 0 12 x + 3 z = -10 27 x – 3 z = 36 39 x = 26 x = 2/3 Step 3: 12 x + 3 z = -10 12(2/3) + 3 z = -10 3 z = -18 z = -6 Step 4 8 y + z = 0 8 y + (-6) = 0 8 y = 6 y = 3/4
Solving Inconsistent Systems with Three Variables Solve the system: 2 x – 4 y + 6 z = 5 -x + 3 y – 2 z = -1 x – 2 y + 3 z = 1 Solution: Eliminate x in equations 1 and 3 2 x – 4 y + 6 z = 5 2 x – 4 y + 6 z = 2 0 x + 0 y + 0 z = 3, so 0 = 3. If you receive a statement that is not true, the equations are parallel with each other. You can stop the entire question as there will not be an answer that satisfies all three equations.
Practice Problems: Solve the following systems 1) 2) x – 5 y + 2 z = 4 3 x + y – z = 6 -2 x + 10 y – 4 z = 7 4 x – 8 y = -7 4 y + z = 7 -8 x + z = -4
Student Survey Please complete honestly! https: //forms. office. com/Pages/Response. Page. a spx? id=i. Fj. Xcqx 7 e 0663 YUcpvf 1 u 3 Wg 8 v 97 Iw 1 Am OKI 3 ZWQRc 9 UQUw 0 RU 5 OWk. FKSEg 4 TTVFU 0 k 5 Wjh. MREd. MMS 4 u
- Slides: 7