A person with no more than $15,000 to invest plans to place the money in two investments. One investment is high-risk, high yield; the other is low risk, low yield. At least $2,000 is to be placed in the high-risk investment. Furthermore, the amount invested at low risk should be at least three times the amount invested at high-risk. Find a system of inequalities that describes all possibilities for placing the money in the high- and low-risk investments.

let x be high risk investment

and y be low risk investment
so x + y < 15000
y>3x
x> 2000

To find the system of inequalities that describes all possibilities for placing the money in the high-risk and low-risk investments, we need to consider the given conditions:

1. At least $2,000 is to be placed in the high-risk investment.
2. The amount invested at low risk should be at least three times the amount invested at high-risk.
3. The total investment should not exceed $15,000.

Let's denote the amount invested in the high-risk investment as "x" (in dollars) and the amount invested in the low-risk investment as "y" (in dollars).

Based on the given conditions, we have:

1. x ≥ 2000 (At least $2,000 needs to be placed in the high-risk investment).

2. y ≥ 3x (The amount invested at low risk should be at least three times the amount invested at high-risk).

3. x + y ≤ 15000 (The total investment should not exceed $15,000).

Therefore, the system of inequalities that describes all possibilities for placing the money in the high-risk and low-risk investments is:

x ≥ 2000
y ≥ 3x
x + y ≤ 15000