Answer:
(x , y , z) = (6 , 5 , -6)
Step-by-step explanation:
We can not deal with three equations at once. So the overall thinking process:
- Take two of them in turn (whichever you like)
- Eliminate one variable, in order to be left with a system of two equation with two variables
- Solve the previous system
- Go to the equation you left intact at the beginning and substitute the two of the three variables you found before, in order to calculate the third one
In other words...
(1) -4x + 5y + 2z=-11
(2) -2x + 2y – 2z = 10
(3) 5x – y + 2z = 13
(1) + (2) =>
-4x -2x + 5y + 2y + 2z - 2z = -11 + 10 => -6x + 7y = -1 (4)
(2) + (3) =>
-2x + 5x + 2y - y - 2z + 2z = 10 + 13 => 3x + y = 23 => 6x + 2y = 46 (5)
(4) + (5) => -6x + 6x + 7y + 2y = -1 + 46 => 9y = 45 => y = 5
(y = 5) (5) => 6x + 10 = 46 => x = 6
(x = 6 , y = 5) (3) => 5 * 6 - 5 + 2z = 13 => 30 - 5 + 2z = 13 => 2z = 13 - 25
=> 2z = -12 => z = -6
