The price of one kaya bun is RMx and the price of one butter bun is RMy. Suzi buys 6 kaya buns and 3 butter buns while Fauzi buys 4 kaya buns and 5 butter buns. Suzi pays RM8.40 and Fauzi pays RM1 less than Suzi. Using the matrix method, calculate the price of one kaya bun and the price of one butter bun.

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To determine the prices of one kaya bun (**RMx**) and one butter bun (**RMy**), we can set up a system of linear equations based on the purchases made by Suzi and Fauzi. We'll then solve this system using the matrix method.

### Step 1: Formulate the Equations

From the problem:

1. **Suzi's Purchase:**
   $$
   6x + 3y = 8.40
   $$
   
2. **Fauzi's Purchase:**
   $$
   4x + 5y = 7.40
   $$
   *(Note: Fauzi pays RM1 less than Suzi, so $$8.40 - 1 = 7.40$$)*

### Step 2: Represent as a Matrix Equation

The system can be written in matrix form as:
$$
\begin{bmatrix}
6 & 3 \
4 & 5 \
\end{bmatrix}
\begin{bmatrix}
x \
y \
\end{bmatrix}
=
\begin{bmatrix}
8.40 \
7.40 \
\end{bmatrix}
$$

### Step 3: Find the Inverse of the Coefficient Matrix

Let $$ A = \begin{bmatrix} 6 & 3 \ 4 & 5 \end{bmatrix} $$ and $$ \mathbf{b} = \begin{bmatrix} 8.40 \ 7.40 \end{bmatrix} $$.

First, compute the determinant of $$ A $$:
$$
\text{det}(A) = (6)(5) - (4)(3) = 30 - 12 = 18
$$

The inverse of $$ A $$ is:
$$
A^{-1} = \frac{1}{\text{det}(A)} \begin{bmatrix} 5 & -3 \ -4 & 6 \end{bmatrix} = \frac{1}{18} \begin{bmatrix} 5 & -3 \ -4 & 6 \end{bmatrix}
$$

### Step 4: Multiply the Inverse by Vector $$ \mathbf{b} $$

$$
\begin{bmatrix}
x \
y \
\end{bmatrix}
= A^{-1} \mathbf{b}
= \frac{1}{18} \begin{bmatrix} 5 & -3 \ -4 & 6 \end{bmatrix} \begin{bmatrix} 8.40 \ 7.40 \end{bmatrix}
$$

Calculating the products:
$$
x = \frac{1}{18} (5 \times 8.40 - 3 \times 7.40) = \frac{1}{18} (42.00 - 22.20) = \frac{19.80}{18} = 1.10
$$
$$
y = \frac{1}{18} (-4 \times 8.40 + 6 \times 7.40) = \frac{1}{18} (-33.60 + 44.40) = \frac{10.80}{18} = 0.60
$$

### Conclusion

- **Price of one kaya bun (x):** RM **1.10**
- **Price of one butter bun (y):** RM **0.60**

**Answer:**  
One kaya bun costs RM 1.10 and one butter bun costs RM 0.60.
One kaya bun costs RM 1.10 and one butter bun costs RM 0.60.

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