# 9.6.1. Solving Two First-Degree Equations Algebraically and Geometrically

The cost of 2 pens and 2 books is LE. If the number of pens increases by 2 and the number of books decreases by 1, the cost becomes LE. Find the cost of one pen and that of one book.

• A a book LE, a pen LE
• B a book LE, a pen LE
• C a book LE, a pen LE
• D a book LE, a pen LE

### Example

The cost of 2 pens and 2 books is LE. If the number of pens increases by 2 and the number of books decreases by 1, the cost becomes LE. Find the cost of one pen and that of one book.

### Solution

Denote the cost of one pen by and the cost of one book by .

If the cost of 2 pens and 2 books is , then

The cost of 4 pens and 1 book is , so

The second equation can be arranged to give

Substituting this expression for into the first equation gives an equation which can be solved for .

Finally, substitute this value of back into the equation for .

Therefore, the cost of one book is and the cost of one pen is .

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