Let's denote the price of the first book as \( x \) and the price of the second book as \( y \).
Based on the information given, we can write the following equations:
#1: The total cost of the two textbooks is $65. \[ x + y = 65 \]
#2: The difference in price between the two books is $9. \[ x - y = 9 \]
Now we can solve these equations to find the values of \( x \) and \( y \).
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From the first equation, we have: \[ y = 65 - x \]
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Substitute \( y \) in the second equation: \[ x - (65 - x) = 9 \] \[ x - 65 + x = 9 \] \[ 2x - 65 = 9 \] \[ 2x = 74 \] \[ x = 37 \]
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Now substitute \( x \) back into the first equation to find \( y \): \[ 37 + y = 65 \] \[ y = 65 - 37 = 28 \]
So, the prices of the books are:
- The cost of the first book (x) is $37.
- The cost of the second book (y) is $28.
In summary: Let \( x = 37 \) (first book), Let \( y = 28 \) (second book).