Question

-4x + 5y + 2z=-11
-2x + 2y – 2z = 10
5x – y + 2z = 13​

Answer 1

(x , y , z) = (6 , 5 , -6)

Explanation:

We can not deal with three equations at once. So the overall thinking process:

1. Take two of them in turn (whichever you like)
2. Eliminate one variable, in order to be left with a system of two equation with two variables
3. Solve the previous system
4. 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