A  saleswoman earned a fixed salary of Kenya shillings x and a commission of Kenya shillings y. In a certain she sold 30 items and earned a total of 50,000 Kenya shillings.the following months she sold 40items and earned a total 56,000 Kenya shillings.

Let's go through the problem step by step to form the system of equations and then solve it using the matrix method.

### Problem Restatement:
- A saleswoman earns a fixed salary of \( x \) Kenya shillings and a commission of \( y \) Kenya shillings per item sold.
- In a certain month, she sold 30 items and earned a total of 50,000 Kenya shillings.
- In the following month, she sold 40 items and earned a total of 56,000 Kenya shillings.

### Step 1: Form Two Equations
For the first month:
\[
x + 30y = 50000
\]
For the second month:
\[
x + 40y = 56000
\]

### Step 2: Solve the Equations Using the Matrix Method
We can represent the system of equations in matrix form as follows:

\[
\begin{pmatrix}
1 & 30 \\
1 & 40 \\
\end{pmatrix}
\begin{pmatrix}
x \\
y \\
\end{pmatrix}
=
\begin{pmatrix}
50000 \\
56000 \\
\end{pmatrix}
\]

To solve this system, we'll use the matrix method, which involves finding the inverse of the coefficient matrix and multiplying it by the constants matrix.

Let's solve this now.

Learn how to solve a system of linear equations using matrices. This problem involves determining a saleswoman's fixed salary and commission per item sold based on her earnings from selling 30 and 40 items in consecutive months. Suitable for high school students studying linear equations and matrix algebra.

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