Question

The cost of 2 pencils and 3 erasers is Rs. 9 and the cost of 4 pencils and 6 erasers is Especially. 18. Find the cost of each pencil and each eraser.​

Answer 1

Let the cost of one pencil =Rs x

and cost of one eraser =Rs y

According to the question

$2x+3y=9 ...(1)$

$4x+6y=18$

$⇒2(2x+3y)=18$

$⇒2x+3y=9...(2)$

As we can see from Eq. (1) and (2)

$⇒ \frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$

∴ Given pair of linear equations has indefinitely many solutions.

Answer 2

Given,

The cost of $2$ pencils and $3$ erasers is $9$.

Let the cost of pencil be $x$

Let the cost of eraser be $y$

This can be written in the equation as

$2x+3y=9$

$2x=9-3y$

$x=\frac{9-3y}{2}$

The cost of $4$ pencils and $6$ erasers is $18$

This can be written in the equation as

$4x+6y=18$

Here substitute the value of $x$ in the above equation.

we get,

$4(\frac{9-3y}{2} )+6y=18$

$2(9-3y+3y)=18$

18=18

For the given pair of linear equations has indefinitely many solutions.

Therefore, it has many solutions.