Question 1205323
## Setting up the Linear Model

**Let's denote:**
* **G:** Amount invested in Gading Mutual Deposit
* **M:** Amount invested in Maju Makmur Bar Gold
* **I:** Amount invested in Indah Certificate Deposit
* **S:** Amount invested in Selamat Maju Bar Gold

**Based on the given information, we can set up the following system of linear equations:**

1.  **Total Investment:** G + M + I + S = 450000
2.  **Total Annual Return:** 0.09G + 0.06M + 0.10I + 0.15S = 0.08 * 450000
3.  **Indah and Selamat Maju Investment:** I + S = (1/3) * 450000

## Solving the System Using Elimination Method

**Step 1: Simplify the Equations**
* Equation 2: 9G + 6M + 10I + 15S = 360000
* Equation 3: I + S = 150000

**Step 2: Eliminate a Variable**
* Let's eliminate S. From Equation 3, we can express S as:
  * S = 150000 - I
* Substitute S in Equations 1 and 2:
  * Equation 1: G + M + I + (150000 - I) = 450000
    => G + M + 150000 = 450000
  * Equation 2: 9G + 6M + 10I + 15(150000 - I) = 360000
    => 9G + 6M - 5I = -750000

**Step 3: Simplify the Equations Further**
* Equation 1: G + M = 300000
* Equation 2: 9G + 6M - 5I = -750000

**Step 4: Eliminate Another Variable**
* Let's eliminate M. Multiply Equation 1 by -6 and add it to Equation 2:
  * -6G - 6M = -1800000
  * 9G + 6M - 5I = -750000
  * -------------------------
  * 3G - 5I = -2550000

**Step 5: Solve for G and I**
* From Equation 1, we can express M as:
  * M = 300000 - G
* Substitute M in the simplified Equation 2:
  * 3G - 5I = -2550000
  * 3G - 5(150000 - G) = -2550000
  * 8G = 1200000
  * G = 150000
* Substitute G in M = 300000 - G:
  * M = 300000 - 150000 = 150000
* Substitute G in I + S = 150000:
  * I + S = 150000
  * I + (150000 - I) = 150000
  * S = 0

Therefore, the investments are:
* Gading Mutual Deposit: RM150,000
* Maju Makmur Bar Gold: RM150,000
* Indah Certificate Deposit: RM150,000
* Selamat Maju Bar Gold: RM0