From the wear on the small chainring, and how poorly the chain is sitting on the big chainring in your pictures, the chain is probably seriously worn out, and you'll find the freewheel cogs are worn out as well. If you replace the chain, it'll skip over the cogs in the rear under load. If you choose not to replace your chain, you'll wear out the big chainring too.

If money is Seriously tight, you could put off the drivetrain replacement until it starts skipping again or your chain snaps, but it won't be a good time when it does. That rear tire probably won't last long either.