Solve the system of equations using matrices. use gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2

X + y + z = -5
x - y + 3z = -1
4x + y + z = -2

let's get rid of all the y's. 

add these two equations...

      x + y + z = -5
+    x - y + 3z = -1

2x + 4z = -6
2x = -6 - 4z
x = -2z -3

then add the last two equations..
       x - y + 3z = -1
+     4x + y + z = -2

5x + 4z = -3
4z = -5x -3
z = -5/4 - 3/4

substitute x = -2z -3 to any of the equations
-2z - 3 + y + z = -5
-z - 3 + y = -5
y = -2 + z

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.