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.