X + y + z = 12

6x - 2y - z = 16

3x + 4y + 2z = 28

x = 4

y = 0

z = 8

Step-by-step explanation:

Step 1: Multiply first equation by - 6 and add the result to the second equation. The result is:

x3 x+y - 8y + 4y + z - 7z + 2z = 12 = - 56 = 28

Step 2: Multiply first equation by - 3 and add the result to the third equation. The result is:

x + y - 8 y + y + z - 7 z - z = 12 = - 56 = - 8

Step 3: Swap Row 2 and Row 3. After this step we have:

x + y + y - 8 y + z - z - 7 z = 12 = - 8 = - 56

Step 4: Multiply second equation by 8 and add the result to the third equation. The result is:

x + y + y + z - z - 15 z = 12 = - 8 = - 120

Step 5: solve for z.

-15 zz=-120=8

Step 6: solve for y.

y-zy-8=-8y=-8=0

Step 7: solve for x by substituting y=0 and z=8 into the first equation