SOLUTION: A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility. Some of the money was borrowed at 6%, some at 7%, and some at 10%. Use a system of linear

Algebra ->  Matrices-and-determiminant -> SOLUTION: A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility. Some of the money was borrowed at 6%, some at 7%, and some at 10%. Use a system of linear      Log On


   

Question 1120168: A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility. Some of the money was borrowed at 6%, some at 7%, and some at 10%. Use a system of linear equations to determine how much was borrowed at each rate given that the total annual interest was $144,000 and the amount borrowed at 6% was twice the amount borrowed at 10%. Solve the system of linear equations using matrices.

WORK I'VE ALREADY DONE (Please advise):
I've come up with the following equations
x+y+z=2000000
0.06x+0.07y+0.10z=144000
y=4z
with the following matrix:
[1,1,1]* [2000000]* [x]
[0.06, 0.07, 0.10]* [144000]*[y]
[0,1,-4]*[0]*[z]
To get the following answers: 500000,1200000,300000
Please tell me what I'm doing wrong.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First and second equations look good.
y is twice z, why do you have the equation with y equal to 4 times z?
Correct that and find the solution.