5 pens and 2 notebooks cost 34 dollars. 3 pens and 4 notebooks cost 40 dollars.

Step 1. The pair. $5p + 2n = 34$ and $3p + 4n = 40$.

Step 2. Make the notebooks match. Doubling the first: $10p + 4n = 68$.

Step 3. Subtract. $(10p + 4n) - (3p + 4n) = 68 - 40$, so $7p = 28$ and $p = 4$ dollars.

Step 4. The notebook. $20 + 2n = 34$, so $n = 7$ dollars.