Question

If the cost of $2$ pencils and $3$ erasers is $Rs.9$ and the cost of $4$ pencils and $6$ erasers is $Rs.18$ . Find the cost of each pencil and each eraser.

Answer 1

Find the cost by forming linear equations

Let $x$ be the cost of a pencil and $y$ be the cost of a eraser

Then from given information

$$\begin{gathered} 2x+3y=9......\left(1\right) \\ 4x+6y=18.....\left(2\right) \end{gathered}$$

From equation $\left(1\right)$ and $\left(2\right)$

we can see that ratio of coefficients is same

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

The pair of linear equation has infinitely many solution.

Hence, infinitely many cost of pencil and eraser is possible .