Question

Romila went to a stationery shop and purchased 2 pencils and 3 erasers for ₹ 9. Her friend, Sonali saw the new variety of pencils and erasers with Romila and she also bought 4 pencils and 6 erasers of the same kind for ₹ 18. Represent this situation algebraically and graphically.

Answer 1

Let the cost of 1 pencil be x and cost of 1 eraser be y.

According to question,

2x + 3y = 9 …(1)

and 4x + 6y = 18 …(2)

The algebraic representation of this situation is 2x + 3y = 9, 4x + 6y = 18.

For representation of these equations graphically, we draw the graph of these equations as follows :

2x + 3y = 9

⇒ 3y = 9 – 2x

⇒ y = \(\frac{9−2x}{3}\)

We put the different values of x in this equation then we get different values of y and we prepare the table of x, y for the equation 2x + 3y = 9.

Table-1

and 4x + 6y = 18

⇒ 6y = 18 – 4x

⇒ y = \(\frac{18−4x}{6}\)

Now, we put the different values of x in this equation then we get different values of y and we prepare the table of x, y for the equation 4x + 6y = 18.

Table-2

Now, we plot the values of x and y from Table-1 and Table-2 on the graph paper and we draw the graphs those passes through these values.