If both supply and demand increase at the same time, will prices rise as well?I need to explain it in relationship to the supply and demand curves.

This will depend on whether the supply and the demand rise
at the same rate or whether one or the other rises more
quickly.

If supply rises
faster than demand, the equilibrium price of the good will go down.  The supply curve
will move to the right a given amount.  The demand curve will also move to the right,
but not as much.  This will lead to a lower equilibrium price than
before.

If demand rises faster
than supply, the opposite of the above will be true.  Both curves still move to the
right, but the demand curve moves more and therefore the price
rises.

So this really depends on the degree to which each
of the two curves on your graph moves.