4x + 4y + z = 24
2x - 4y+z=0
5x – 4y - 5z = 12
(show steps)

See below

Explanation:

4x + 4y + z = 24 (1)
2x - 4y + z = 0 (2)
5x - 4y - 5z = 12 (3)

Add (1) and (2):

4x + 4y + z = 24
2x - 4y + z = 0
————————
6x + 2z = 24 (4)

Add (1) and (3):

4x + 4y + z = 24
5x - 4y - 5z = 12
————————-
9x - 3z = 36 (5)

Add (4) and (5):

3(6x + 2z = 24)
2(9x - 3z = 36)
————————
18x + 6z = 72
18x - 6z = 72
———————-
36x = 144
x = 144/36
x = 4

Plug x value in (4):

6(4) + 2z = 24
24 + 2z = 24
2z = 0
z = 0

Plug x and z value in (2):
2(4) - 4y + 0 = 0
8 - 4y + 0 = 0
-4y = -8
y = -8/-4
y = 2

Therefore, x = 4, y = 2 and z = 0

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.

the answer is 18.