Question : The coach of a cricket team buys 3 bats and 6 balls for Rs 3900. Later, she buys another bat and 2 more balls of the same kind for Rs 1300. Represent this situation algebraically and geometrically.
Solution : Let us denote the set of one bat by Rs x and one ball by Rs y. Then, the algebraic representation is given by the following equations :
3x + 6y = 3900 โฆโฆ.(1)
and x + 2y = 1300 โฆ..(2)
To obtain the equivalent geometric representation, we find two points on the line representing each equation. That is, we find two solutions of each equation.
These solutions are given below in the table.
For 3x + 6y = 3900
x
0
1300
y
650
0
For x + 2y = 1300
x
500
100
y
400
600
We plot the points A(0, 650) and B(1300, 0) to obtain the geometric representation of 3x + 6y = 3900 and C(500, 400) and D(100, 600) to obtain the geometric representations of x + 2y = 1300.
We observe that these lines are coincident.
