SOLUTION: Solve the following simultaneous equations a. 2x+3y-z= 13 x -2y+2z=-3 3x+y +z =10 b. x-3y+z = -2 x+y-2z = 4 -2x+y+z= 12

Algebra ->  College  -> Linear Algebra -> SOLUTION: Solve the following simultaneous equations a. 2x+3y-z= 13 x -2y+2z=-3 3x+y +z =10 b. x-3y+z = -2 x+y-2z = 4 -2x+y+z= 12      Log On


   

Question 1165929: Solve the following simultaneous equations
a. 2x+3y-z= 13
x -2y+2z=-3
3x+y +z =10
b. x-3y+z = -2
x+y-2z = 4
-2x+y+z= 12
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the following simultaneous equations
a. 2x+3y-z= 13
x -2y+2z=-3
3x+y +z =10
--------------------
2x+3y-z= 13 ----- Eqn 1
3x+y +z =10 ----- Eqn 3
--------------------------- Add
5x + 4y = 23
===================
4x +6y-2z= 26 ----- Eqn 1 times 2
x -2y+2z=-3 ----- Eqn 2
------------------------------ Add
5x + 4y = 23
Same result ---> no unique solution.
| 2   3  -1|
| 1  -2   2|
| 3   1   1|

Det = 2*(-2*1 - 1*2) - 3*(1*1 - 3*2) -1*(1*1 - 3*-2) = -8 + 15 - 7 = 0
No solution.
==============================================
b. x-3y+z = -2
x+y-2z = 4
-2x+y+z= 12