How do you solve this problem using linear equations with two variables?

Question

Q: A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The investor wants an annual interest income of $990 from the investments. What is the most that can be invested in the 7.5% bond?

Would the equations be
12,000 = 9x + 7.5y
and
990 = x + y ? Is this right?

Also, what exactly is interest and investment?

Answer 1

Callx the money you invest to obtain 7.5% and y the one for 9%

x+y=12,000.
The yield of each investment is 7.5/100 *x and 9/100*y .the sum must be 990
So you have the system
x+y=12,000
7.5*x+9*y=99000
7.5*x +9*(12,000-x) = 99000=====> x=6,000( Your answer

If you have some money you don´t use and you lend it this is an investment.
The nreceiver pay you a certain sum for using YOUR money.
This is called interest..

Answer 2

If x=the amount invested at 9% and y=the amount invested at 7.5%, your equations would be

x+y=12000
.09x+.075y=990

If you invest x dollars at 9% interest, it will earn .09x dollars. Ditto for y and 7.5%.

Solving:
9x+9y=108000
-(9x+7.5y=99000)
______________
1.5y=9000
so y=6000

Plugging into the first equation gives x=6000. Therefore, your answer is $6000.