Help on Solving with System Equations

Question: Suppose $10000 is invested in three different investment vehicles paying 5%, 7%, and 9% annual interest. Find the amount invested at each rate if the interest earned after 1 yr is $760 and the amount invested at 9% is equal to the sum of the amounts invested at 5% and 7%.

My anwser:

x + y + z = 10000

.05x + .07y + .09z = 760

z = ?

Help on the third line to my answer because i have to solve.

Re: Help on Solving with System Equations

Re: Help on Solving with System Equations

well i have to solve using inverse matrices

Re: Help on Solving with System Equations

You can do that, or

x + y + z = 10000

.05x + .07y + .09z = 760

z=x+y

making a substitution

x + y + (x+y) = 10000

.05x + .07y + .09(x+y) = 760

now it's two equations with 2 variables.