Why is it negative 9 rather than positive 9 in our first equation

In our first equation for Mesh 1, we assumed a clockwise current $I_1$. When we traverse the $9 \, V$ source in this clockwise direction, we move from its positive terminal to its negative terminal. This represents a voltage drop.

Therefore, according to the standard sign convention for KVL, a voltage drop is assigned a negative sign, which is why it's written as $-9 \, V$.