Problem 8 (Second Session 2001)
To buy two copybooks and three pens, we must pay 9000 LL.
To buy four copybooks and two pens, we must pay 8000 LL.
The preceding givens are translated by the following system:
2x + 3y = 9000
4x + 2y = 8000
1. What do x and y represent in this system?
2. What is the information translated by the equation 2x + 3y = 9000?
3. Calculate the price of a copybook and the price of a pen.

Explanation:

1. x represent the copybook while y represent the pen that is bought.

2. 2x + 3y = 9000 means that in order to buy 2 copybooks and 3 pen you have to pay 9000 LL.

3. Solve for the price of x and y

2x + 3y = 9000 (1)
4x + 2y = 8000 (2)

Multiply (1) by -2:

-2(2x + 3y = 9000)
4x + 2y = 8000
——————————
-4x - 6y = -18000
4x + 2y = 8000
—————————
-4y = -10000
y = -10000/-4
y = 2500

Substitute y value into (2):

4x + 2(2500) = 8000
4x + 5000 = 8000
4x = 3000
x = 3000/4
x = 750

Therefore, 1 copy book = 750LL and 1 pen = 2500 LL