Please explain "basic back-up"?
Backup is the primary function of the PowerWall (PW): when the utility grid fails for whatever reason, the power wall nearly instantly takes over powering at least some of your home. It keeps your critical circuits alive during a grid outage.
One of the things it keeps alive is your solar. Without the PW, your solar stops when the grid goes down. In contrast, PW disconnects you from the grid and will allow your solar to continue working during day time, to both support the house and to recharge the PW. Depending on the size of your solar, season and weather, and your electric usage, PW may be able to keep your house running during an outage lasting many days.
Without PW, when the grid goes down, you go dark.
For most of us, though, while this is a great convenience, it doesn't happen often and has little financial impact. If this was the only benefit, it would be hard to justify economically. Since PW can also allow you to take advantage of lower rates under a Time-of-Use rate plan, and can help you buy only the lowest cost power, it can reduce your electric bill, and hence help to offset the cost of the PW.
There is a Cost Savings mode on the PW, which completely automates its behavior. Once you input your electric rate plan schedule and prices, PW does what it can to save you some $. Set it and forget it.
To summarize:
Solar saves you some money on your electric bill.
PowerWall will protect you against power outages and save you some more money on your electric bill.