How would an increase in the sympathetic nervous system increase stroke volume?

Sympathetic nerves also innervate the myocardium, increases in sympathetic activity increase myocardial contractility and, therefore, increase stroke volume.

Explanation:

The sympathetic nervous system is one of the divisions of the autonomic nervous system. It involuntarily regulates many actions, including the contraction of smooth muscles and the secretion of many glands. Its effects are generally opposite to those of the parasympathetic nervous system. The most important neurotransmitters of the sympathetic system are adrenaline and noradrenaline. Their main action is related to a fight or flight response to external stimuli that can endanger the body, for this reason it increases the frequency and strength of the heartbeat, dilates the bronchial tubes of the lung, dilates the pupil, increases blood pressure, dilates the blood vessels that supply blood to the skeletal muscles throughout the body and stimulates the production of sweat by the sweat glands. This set of actions can be considered as a preparation for fighting or running away, but they are automatically triggered by any intense stimulus such as a shock, a shooting pain or an anxiety generating situation.

A stroke is a disease that affects the arteries leading to and within the brain. It occurs when a blood vessel that carries oxygenated blood to the brain is either blocked by a clot or bursts. So, since the sympathetic nervous system increases the frequency of the heartbeat and blood pressure, this could lead to the bursts of a blood vessel which will cause an stroke.