Obtain an equivalent system by performing the stated element

Obtain an equivalent system by performing the stated elementary operation on the system. Replace the fourth equation by the sum of itself and 3 times the second equation x - 2y + 5z - 6w = 4 4y - z - 4w = -5 3y - 4z + 2w = -3 5y - 5z - 2w = 8 x - 2y + 5z - 6w = 4 12y - 3z - 12w = -15 3y - 4z + 2w = -3 5y - 5z - 2w = 8 x - 2y + 5z - 6w = 4 4y - z - 4w = -5 3y - 4z + 2w = -3 17y - 8z - 14w = -7 x - 2y + 5z - 6w = 4 4y - z - 4w = -5 3y - 4z + 2w = -3 12y + 3z - 14w = -7 x - 2y + 5z - 6w = 4 4y - z - 4w = -5 3y - 4z + 2w = -3 -7y + 8z + 10w = 23

Solution

x - 2y + 5z - 6w = 4                    (1)

     4y - z - 4w = -5                     (2)

    3y  - 4z + 2w = -3                    (3)

    5y - 5z - 2w = 8                    (4)

we need to replace equation-4 by equation-4 + 3 times equation-2.

3 times of equation-2 is

3 * (4y - z - 4w = -5)

12y - 3z -12w = -15        // multiply each term by 3.

now add it with eq-4

12y - 3z -12w = -15

5y - 5z - 2w = 8             adding we get

17y - 8z - 14w = -7