3 notebooks and 2 pens cost ₹110, and 2 notebooks and 5 pens also cost ₹110. Using the matrix method, what is the price of one notebook?

Explanation

1. 01

   With notebook ₹$n$ and pen ₹$p$: $3n + 2p = 110$ and $2n + 5p = 110$, so $A = \begin{bmatrix} 3 & 2 \\ 2 & 5 \end{bmatrix}$ and $|A| = 11$.

2. 02

   $\begin{bmatrix} n \\ p \end{bmatrix} = \frac{1}{11}\begin{bmatrix} 5 & -2 \\ -2 & 3 \end{bmatrix}\begin{bmatrix} 110 \\ 110 \end{bmatrix} = \begin{bmatrix} 30 \\ 10 \end{bmatrix}$.

3. 03

   A notebook costs ₹30 and a pen ₹10.