SOLUTION: Can someone please explain to me how they came to this answer for this problem: I want to understand it because i got it wrong in my exam..... A bakery sells three types of

Question 85537: Can someone please explain to me how they came to this answer for this problem:
I want to understand it because i got it wrong in my exam.....

A bakery sells three types of cakes, each requiring the amount of ingredients shown.
*I separated the porportions by "/" since I couldn't do the table.
Ingredients/Cake1/Cake 2/Cake 3
Flour(cups)/2 /4 / 2
Sugar(cups)/2 /1/2
Eggs/2/1/3
To fill its orders for these cakes, the bakery used 72 cups of flour, 48 cups of sugar, and 50 eggs. How many cakes of each type were made?
Answ.18 cake I, 8 cake II, 2 cake III

Answer by stanbon(48558) (Show Source):
You can put this solution on YOUR website!
Ingredients/Cake1/Cake 2/Cake 3
Flour(cups)/2 /4 / 2
Sugar(cups)/2 /1/2
Eggs/2/1/3
To fill its orders for these cakes, the bakery used 72 cups of flour, 48 cups of sugar, and 50 eggs. How many cakes of each type were made?
Answ.18 cake I, 8 cake II, 2 cake III
-----------------------------
Number of Cakes: x=Cake1,y=CakeII,z=CakeIII
Flour Equation: 2x+4y+2z=72
Sugar EQUATIOn: 2x+ y+2z=48
Eggs EQUATIOn: 2x+ y+3z=50
--------------------
Solve for x,y,z
I used the matrix equation A^1B to get x=18,y=8,z=2
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Cheers,
Stan H.